Dialogue delivery and the blinking
I couldn't understand what he said in Fantastic Beasts quite a few times (and no its not because he has a British accent). This happened in The Danish Girl and Jupiter Ascending as well. What surprises me is that the filmmakers didn't get this fixed , as is usual with post-production ADR (Additional Dialogue Recording). I think his Oscar might be doing him a disservice if people around him don't ask him to fix blips in his performance. Case in point- Eddie's eyelids were fluttering like mad in FBawtft and it really looked quite gimmicky: someone should've told him to show awkward shyness in his acting and not just capturing the outer trappings of awkward shyness. His eyelids pretty much keep blinking like they're sending out a message in Morse code.
Now, I really do think that he has talent (loved him in MWWM) but I still think his performances are still very much about the look of a character: in the Danish Girl he pins his performance on certain sweeping motions of his hands. He's really good at capturing mannerisms but that's just a part of what it takes to do justice to a role. He doesn't move us with the emotions he's depicting. I think his Hawking was very impressive as an impression but not as a performance.