In a 1987 New York Times article, E.J. Dionne reported on a series of blunders by the Delaware Senator that knocked him out of contention.  This list includes plagiarism, misrepresentation of his educational achievements, and telling a voter about his big, big brain:

The tape, which was made available by C-SPAN in response to a reporter’s request, showed a testy exchange in response to a question about his law school record from a man identified only as ”Frank.” Mr. Biden looked at his questioner and said: ”I think I have a much higher I.Q. than you do.”

He then went on to say that he ”went to law school on a full academic scholarship - the only one in my class to have a full academic scholarship,” Mr. Biden said. He also said that he ”ended up in the top half” of his class and won a prize in an international moot court competition. In college, Mr. Biden said in the appearance, he was ”the outstanding student in the political science department” and ”graduated with three degrees from college.”

Well, if we measured political IQ, Biden might barely show up on the scale.  As Dionne notes later in the article, Biden got one degree from college, a double major.  He didn’t get a full scholarship to law school; he got a partial scholarship and received grants to cover the rest.  He didn’t graduate in the top half of his class, as he asserted to “Frank”, whose IQ score has been lost in the mists of time.  In fact, Biden came in 76th in a class of 85 which isn't even close. 

(snip)

What was Biden’s excuse at the time?  “I exaggerate when I’m angry.”