I always tend to find playing dumb or socially inept characters difficult. It's hard when you can figure things out while your character has to keep a blank stare, and then when you want to point things out to your team mates but can't...that can be hard. Also, when your character isn't good with people and you have to be rude, or mumble, or stutter, or whatever when your dealing with a certain person is mission critical. Taking a dive for the sake of staying in character can be tough.
On the other hand, playing a character who's smarter than I am can be a feat when I'm often tired and trying to stay alert through the session. Then trying to act as charming and eloquent as your character can be tough when I'm not much of a Lando Calrissian in real life.
Usually I just have to ham it up and laugh along with my friends.