We know using Creo Animal to create sheep for a temporary, but sufficiently long duration, will leave behind perfectly "mundane" byproducts when they expire: dung, meat, wool (ArM p.77). Does the same hold for Muto? If I change a chicken into a sheep for a sufficiently long time, will the milk and wool it produces (eventually) be "mundane"?
Yes, I'm pretty sure that if you did a clever search of the forums you'd find at least two threads where we've hashed it out with logic and rules quotes. Sadly, I don't feel up to the challenge of marshalling support for my opinion at the moment.
I think the answer is no based on the Limit of Essential Nature.
I've written a post below where I've wrapped up the two issues "Please explain to me how this might work", and "I don't share your opinion and here's why" in a sort of stream of consciousness mess. I think it comes across as unnecessarily argumentative and combative, also it's not as clear as I'd like to be (well, none of my posts are as clear as I'd like but perhaps this one more than most). If I come back later and edit it to soften the tone and/or make it more clear don't be surprised.
I don't see how essential nature comes into it. It is clear that essential nature can be temporarily overcome with magic, otherwise we couldn't have Cloak of Black Feathers, Lungs of the Fish, or a million other spells.
Even if hermetic magic couldn't overcome essential nature we're adding characteristics to the target rather than taking them away. If we want to produce wool by slapping an enchanted device with a constant duration MuAn "transform into sheep" effect in it on things that threaten our PC's (lets say a particularly rambunctious pack of saber toothed turtles,... our item is target group) we're adding the characteristics of being a sheep to the turtles, we're not removing their essential turtle nature. Unless not producing wool is somehow essential to dire-turtle-ness I don't see a conflict. It seems off to me to declare each of the limitless list of characteristics not possessed by given thing as all "essential".
Are you (jebrick) suggesting that after a spell expires all or some of the things that have been produced by a thing during the duration of the muto spell be magically altered? i.e. cheese that was made from the output of a mouse that had been temporarily changed into a dairy cow retroactively becomes mouse-milk cheese at the moment when the mouse regains its true form? Is a transformed wheel of mouse-milk cheese now much much smaller or is it the same size? Or does the former mouse now cow not produce milk at all during the spell?
How far away from the transformed thing does the magic act, if I've made a rhinoceros into a sparrow, does the sparrow poop change into rhino poop? If so, does it do it instantly or at the end of the spell? (or does the sparrow extrude rhinoceros dung rather than sparrow?)
How about footprints? combat wounds? would they also transform back after the spell's expiration? What rostrum are you going to use to draw the line between phenomena that are limited by essential nature and ones that are not?
I'd worry that such a limitation would lead a game down a path of interactions with a magic system that players might see as unnecessarily rulesy, not fun, and specifically designed to hinder their creativity. Meanwhile just saying yes is (or at least seems to me to be) conceptually cleaner and very likely more fun for the players.
Wool, poop, and milk come from an animal, while footprints are something done by an animal, so in any case the footprints would not change.
It seems to me the issue would be duration- is the animal product a direct effect of the changed animal, or is it something produced by the animal processes. For example if you change a turtle to a sheep and immediately harvest the wool, that wool is made by magic and would disappear when the spell expires. If, on the other hand, you transform a turtle into a cow with moon duration, and at the end of that time the grass it was eating as a cow produces milk as a cow, then this is indirectly the same as using rego, acting on natural grass through a natural process emulated by magical means to get a natural product.
Given that we are talking about medieval perception of how things work rather than modern scientific understanding, I would say the first milking is not "real" but subsequent milk is.
I would interpret the cow as a black box machine that turns grass into milk, and thus turning a turtle into a cow for extended duration would create real milk. If I was feeling cheeky, I might argue that some of the magic might leave traces in the milk for minor warping, but by RAW it shouldn't.
Just like if I turned a bucket of paint into an axe and hit a tree, it doesn't turn the chop into a paint-splatter the next day, though that is an extreme example.
Again, all opinion and interpretation. At least once in my home game I've said "The Order of Hermes doesn't have a definitve answer, here are the possibilities hermetic theory has suggested. Go find out."
My answer is that any change in something's essential nature must be maintained (ArM pg 79). Once that magic goes the essential nature comes back.
If your muto'ed turtle sheep produce a lamb, is it still a lamb when the spell ends or a saber-toothed turtle? I say the latter because you can't change the essential nature, just the appearance ( ArM pg 79).
The sparrowRhino poop becomes just rhino poop when the spell ends because the poop only appeared to by sparrow poop because of the magic. Cow milk becomes mouse milk because you just changed the appearance of the mouse. It is still a mouse when the spell wears off.
Now if you had your enchanted device that keeps the magic going then, for all appearances, the turtles are sheep and everything they produce is sheep like. But that stops as soon as the magic ends.
Changes resulting from Muto are temporary but they are real during that temporary period.
Turn a person into a cow and she's a real cow, producing real milk, until the spell expires. Turn her into a sparrow and she produces real sparrow poop. Once these substances are out of her body they are no longer part of her, and therefore no longer subject to the Muto spell. They simply exist, as real substances which are no longer blocked by magic resistance because they're no longer magical.
It's not as if Muto is some sort of dream and everything goes back to the way it was afterwards. It's just magic that wears off after some time.
Sounds like there's strong reasons to go either way, and nobody has quoted explicit rules proof either way. Looks like your saga may vary, and each answer creates interesting ideas. Shearing your turtle could be fun.
The offspring question is an interesting one, since that should result in a mixing of essential natures, not temporary forms. So if you transform a bull into a man and he gets a woman pregnant the result should be a minotaur. Depending on the reproductive cycles involved (changing the male seems like the way to go) this could be a cheap source of magical creatures...
I would think, for my own sanity, that basic Muto spells won't allow for successful reproduction... Though some past canon may suggest otherwise. Experimentation, side effects, magical or faerie beasts may have different results. YSMV.
Brief resurrection of this thread: I just got a copy of Magi of Hermes via Bundle of Holding, and the first fellow in there is Alexander of Jerbiton, who turns into animals while exploring North Africa. Here's a brief excerpt from his cobra spell:
It's up to your saga if this came from the laws of Hermetic Magic, or a side-effect from him experimenting to learn this spell.
Hmm. Interesting.
Note that MoH does state when stuff is the product of experimentation; and indeed seems to use experimentation as a way to "cover" some cool effects that may, or may not be by the rules depending on the interpretation given by a particular troupe. One such example is Scipio's bottomless bag. In the case of Alexander's poison, no experimentation is mentioned, so one should assume that the result should be considered "standard" by Hermetic magic. Then again, MoH is replete with errors and questionable interpretations of the rules, so ...
In any case, note that the original question was about byproducts "after sufficient time has passed". I'll be happy to leave alone the question of whether the milk from a fly transformed into a cow for D:Diam stays milk after the spell expires, as long as I get an answer about the milk from a fly that has been "cowed" for, say, a few days. It seems that there's a rough consensus (with a small handful of exceptions) that Muto does behave like Creo: the byproducts of stuff that's been transformed for "sufficient" (and there lies the rub) time are natural and do not change back when the spell expires.
By this interpretation, since special results from experimentation are repeatedly explicitly stated in MoH, with no special results mentioned one should assume Scipio's bottomless bag only benefited from the experimentation's bonus to the lab total. As an added point, based on the number of experiments, the number of special results of one sort or another that are explicitly mentioned fit very well into the total number of such special results by the odds.
Nice spot. At very least I would have expected the results of consuming food and similar to have real results. This one is on the edge and is interesting, maybe pushing the edge a little too far for many.
Neither of these points can be used to argue -- especially on such small numbers -- that explicitly mentioned results are all results.
However, I seem to recall that at some point someone said that during playtesting of MoH, Scipio's bag caused a lot of controversy. It was a cool effect, but also something that several people thought was against the rules. The glamour mystery has very little to do about it, as many of the same arguments can be made about "vanilla" Hermetic magic guidelines to give something a "major unnatural property". So the final stance of David Chart was to make it the result of experimentation without explicitly saying anything about it. In this way some troupes could say no, and some troupes could say "yes, vanilla yes!" to an effect that may, or may not fit the rules (for a wide number of reasons) but certainly fits many tropes of myth.
I freely admit not being able to bring any evidence about this statement, in part because I am too lazy to search for info that may not even be (and probably is not) on this forum! I do not really care about convincing anybody; I am just providing info 
I know that. But look at what I was pointing out more carefully. Note that I said "by this interpretation." Your argument is that since experimentation has been mentioned elsewhere, the lack of mention should be interpreted as it hasn't been done. If we use that same interpretation we get: since special results have been mentioned elsewhere, the lack of mention should be interpreted as they haven't happened. On top of that, I provided an extra bit of evidence for special results.
Even if from somewhere else, I'd love to see it. Because right now we have it working in canon and nothing even vaguely suggesting that it might be from experimentation.
IMO, the "byproducts" (I learned a word today 
) are real. Muto can overcome essential nature. That's why muto magic always must have duration because momentary muto spells do not work : essential nature will come back. But under a Muto spell, essential nature is, essentialy (I'm not sure that word means the same as in french, but the wordplay is too fun to change), put away.
Some byproducts are perhaps more complexes: among them, I first think about (making) babies. For me? no: limit of the soul. Humans cannot create animals who have no souls (hence a magus transformed as cow cannot make a calf if mating with a bull) and animals cannot create being with soul; and only woman can have babies (I think that one is evoked in AnM in the fertility chapter, but I'm not sure).
The "poison from a snake" example from Alexander who has been quoted here seems to me absolutely normal: if you can penetrate with your MuCo(An) a victim, your bite will poison him. If you can penetrate it like that, chances are you could have penetrate him with a spell to turn him into a fish too, so there is not even a fragile problem of power abuse.
Hmm... as far as I understand it, Alexander while transformed into a snake bites a vessel, dripping his poison in it.
Then, the poison is perfectly mundane poison, that outlasts the transformation and does not need to penetrate the MR of the victim.
But if you transform an ant into a lion can that impregnate a lioness, and is the child simply a lion, or a lion/ant hybrid?
For what it's worth, Bjornaer pregnancies are determined solely by the mother's shape at birth, though if the father was an animal and the mother was a maga in human form, the child is soulless and lacks intelligence (though it has Cunning, still.) It's not clear if offspring with an animal mother possess a soul or not.