I don’t see much in this article that is about tweets specifically.
It starts out discussing his syntax, but that’s more a problem with his speeches. His tweets, because of the character limit, tend to follow traditional SVO order. The problems with vocabulary and register aren’t specific to tweets either, but found in everything he says.
(But I find it hard to believe that ASL doesn’t have a sign that’s the equivalent of “dude.” The word has been such an integral part of American speech for so long that ASL signers would have to have an equivalent by now.)