All of us can agree on facial expressions being a challenge… 
Anyway, my experiences: For me, animation is something of a mixed bag, as it really depends on the complexity of your model.
In my case, I normally use human-like rigs for my characters, but recently, I had to do something slightly different to make a whip. believe me, it didn’t take long for me to work out how to animate it, but it did look a little weird at first! 
Overall though, the biggest challenge for all animators is to get the animations looking as natural as possible, especially with humans, but very well applies to dragons, monsters, weird creations you make, etc.
And for me, the longest time-hog at times is having to name all the bones after the rig is finished. For my most recent animated model, I had to come up with names for over 20 bones! (and I reckon 75% of those were in the whips…
)
And another wall a lot of animators, including me, run into is when you go and put the most bad-ass pose on your epic model, but then go “wait what?! why is the arm bending in such a weird shape?!” 
Yes, I am pointing at getting weights right!
In fact, I almost forgot to mention one of my WORST personal animation jobs (The result actually didn’t look too bad though…
) And that was for a dragon-like creature. The bone weights wouldn’t generate because the re-mesh modifier wrecked the topology, so I had to make all the weights manually! 
Overall, the biggest challenge is to get the topology of your model just right, so that when you go to rig your character, any auto-weight tools work smoothly for you! 