According to this 1987 NYT article, Biden didn't just plagiarize part of a speech from a British politician but plagiarized some work during law school.
Also,when he got into an argument with someone who asked about his past he lied that he graduated with three majors (he only had two) that he graduated at the top half of his class (he was 76 out of 85) ans that he had a full scholarship (he had a half scholarship). No big deal? I think it is.
http://query.nytimes.com/gst/fullpage.html?res=9B0DE4D91F3CF931A1575AC0A961948260