I suppose this is another minor issue that I have with the game, where character-defining traits are spread out over distinctions, specialties, and power sets. And what goes where? It defies my nerdy need to categorize everything into boxes.
I love how we all come at these things differently. Spatula, this is actually one of the reasons that I love this game so much. I just really enjoy how you can approach a concept from so many different ways.
I agree with all those above that say there is nothing wrong with adding whatever new thing you want for your table.
Personally, I think the Specialties list in the book covers just about anything that I can think I'd ever want to use...anything else could probably be factored into a Distinction or Power Set somehow.
I also like the idea of very specific Specialties if a player wants a little more flavor for his datafile than he has slots for via Distinctions.
For example, a player that wants his character to have intimate and extensive knowledge of Peace Movements of the 60's...even at Master level, this doesn't break anything. Will it get used a lot? That is totally up to the player that asked for it. I'd think if he felt the need for this to be statted on his datafile, then he'd go to the effort to make it a significant part of his story. [Personally, I'd just recommend the player jot this fact down in the concept/history section of his datafile and we'd roleplay it, but if he REALLY wanted the die...sure, why not?]
But if the question is, do I feel the rule book should expand the list...no, I don't think it is necessary. We can handle that on our own at our own tables.
Most every example that I've seen COULD be shoe-horned into a Specialty we already have...or as others have said, they might fit better as Distinctions.
Entertainment - Are you trying to get a reaction out of a crowd...like acting, singing? I'd say this could be Psych. Knowing and appealing to your audience and trying to sway them would definitely fit into Psych...along with Leadership. Well...if your leadership style is more...aggressive...then you could go with Menace.
Art - Depends on your intended use. Are you trying to speak to an audience with your painting/sculpture/welding/etc? Then, like with Entertainment, I'd go with Psych. Are you trying to scare the bejesus out of people with your insane expression? Menace. Are you trying to sell your art and make a living and a name for yourself in the art community? Business...which would also be used for those entertainers and gamblers that were focusing on making a living with their skills.
Survival, Nature & Animal Handling - I know most of us go to chemistry and physics when we think of science, but just because it isn't our gut reaction, you can't ignore biology, anatomy, kinesiology, botany, entomology, oceanography, nutritional sciences, etc., etc., etc. I think Science covers all of these aspects quite well.
Animal Riding - To me, this is just another form of locomotion...i.e. Vehicles. Vehicle Expert could easily be used for an expert equestrian and cover the handling and care of said "vehicle" as well as knowing contacts and having resources in that field. A Vehicle Master might be a master of all types of biological mounts...especially if you have pegasi (?), unicorns, wargs, battle rhinos or any other form of fantastical critters wandering around your world.
Animal Care - If we aren't talking about a mount (Vehicles) and we don't want to just lump it into Science (Biology), then perhaps you could find your home in Medical (Veterinarian).
Hunting - To me, this is just a form of Combat. You are trying to do harm with hands, weapons &/or traps. For my tastes, I've already lumped Survival and Animal Understanding up in Science.
I think that covers most of what we've seen requested above from my perspective.
Again, remember that character concept is important. Peter Parker is known to be a pretty decent brain in the fields of chemistry and physics, but his datafile doesn't restrict him to those fields. If the table is really that concerned with narrowing down the scope of a Specialty, then they can choose to do so by not trying to use a Specialty for a task that their concepts don't support. [Of course it should be noted that even in the comics, characters step out of their comfort zones all the time and just come up with that fact they need. How many times has Peter dropped some interesting science fact that would more likely come from a biologist?]
It really can be handled on an individual level.
So far, I haven't seen a suggestion for a Specialty that I don't think I couldn't plug into a Specialty we already have.
But what works for your table is the right answer, of course.