Arnold's greatest failing was his vanity.
He was a very effective, and very heroic, field commander, but his personality made him pretty unpopular with his peers and superiors. He wanted into the top reaches of Colonial society, and the chair wasn't being pulled out at the head of the dinner table, so to speak.
Arnold didn't have high regard for Washington, and didn't try to hide it, which really killed him, too. Washington apparently didn't like him, either. That in and of itself was a pretty serious impediment to Arnold's advancement, as the Colonial military heirarchy was really a Cult of Washington.
Peggy Shippen's role may have been overblown in the movie (I missed it), but there's no doubt that she opened the social door for him to people who had Loyalist leanings who likely had a lot more to do with his "conversion" than she did.
Arnold's life after he fled to England wasn't all that great, either. He learned the hard way that if you sell out your side, the side you sell out to never will really trust you, either.