No, McCain's Not Dumb

He just sounds that way at times. Sailer:

The military shrinks gave McCain good marks for mental stability. The main bad-sounding thing that anybody published (other than one embarrassing medical condition) is that he has a "histrionic pattern of personality adjustment" (i.e., he's a big drama queen), but probably anybody who wants to campaign for President is kind of like that.

They tested his IQ twice. I can only find the second (and presumably higher) result. Time wrote in 1999:

Included in the records is a 1984 IQ test. His score, 133, would rank him among the most intelligent Presidents in history.