I have written about learning by observation several times, beginning with Lads Before the Wind in 1975 (reissued with four new chapters in 2000), and the account of two Steno bredanensis, or rough-toothed dolphins, that were inadvertently switched during shows and succeeded in doing most of each other's repertoires, including some shaped behaviors. One animal accepted blindfolds and located and retrieved sinking hoops, a behavior that had taken weeks to train in the model animal. The other animal succeeded in jumping through a hoop high above the water. (They had separate show routines, but could watch each other, day after day, from the holding tanks which had barred underwater gates. Probably sitting there saying "Heck, I could do that!")
They were not perfect, that is, animal #1, who had never worn blindfolds, retrieved one hoop blindfolded instead of all three, and animal #2, who had never done the high hoop jump, missed it on her first attempt, whereupon the trainer with kindly intuition lowered it about six feet and the animal made it on the second try. And they showed no signs of recognizing cues; that, in fact, you always have to teach specifically to each animal, again, see Lads.
More animals than you think can learn by observation IF there is a marker signal in use. An animal that has learned to "try to make you click" by its own behavior; and that then has a chance to see, but not participate in, some other species mate getting clicked for a new behavior...can often, given the opportunity, go out and exhibit the new behavior on the first try. The key element is the click in both cases. [You know what you clicked the first animal for, and you know the second animal has not been clicked for that behavior, and has never exhibited it in your presence.] Without the click, if you see two animals doing the same thing you might be seeing imitation and you might not, and it's very hard to be sure what's going on.
I have reports from many horse trainers that in a barn full of clicker-wise horses, if you teach one horse in the barn aisle to do something new, to hold up a foot, say, the onlookers can and sometimes do offer you the same behavior when they get their turn to be clicked. Same with cats, and in my personal experience clicker-wise cats will sometimes try to do behaviors they saw dogs get clicked for. A lot of the bird clicker people are reporting this event too, unsurprisingly, since many of the smarter birds such as corvids and psitticines show a lot of capacity for mimicry, especially but not limited to acoustic behavior. I have recently written about this in an invited commentary on a paper on culture in marine mammals, for Brain and Behavior, a Cambridge University journal, and I will be glad to give the citation when I know what issue it will be in.
It would be easy enough to do what Cornell calls a "citizens' science" experiment on this matter. Set up the parameters, two clicker-experienced dogs, two behaviors, and a crate. Teach each dog a simple behavior—knock over an empty milk carton, say, or shut a door with the paws—in privacy. Then practice the behavior with one dog, a given number of times, with the other dog crated and watching. Then let the other dog out, put the first dog away, and see what happens. Then reverse the teacher and learner. Would imitation always happen? No. Some would do it, some would not; some would sort-of do it and succeed with some shaping; some would just ignore the whole thing. Can it sometimes happen? Yes, and this is a setup that tends to make that more likely. . With a good data acquisition plan, perhaps including video tape of the model behavior and the first sessions, we could get past this discussion.