I'm reading his part of the Heimskringla right now, and while it's very entertaining, I can't help but feel like it's more of a story told for entertainment than for the purpose of recording what actually happened.
The author seems to be mashing together stories he has heard personally, as well as bits and pieces of other works, but despite the fact that many of these anecdotes are improbable, he makes little effort to try to talk about where they come from, or how accurate they are.
While it's a great piece of literature, one of the most enjoyable medieval primary sources I've ever read, I don't trust it at all. I'm sure that, using Byzantine sources, it's possible to produce a more accurate story of his life in exile. Can someone enlighten me on what that story was, and where I can find more info about it?
What exactly are you not trusting? The written accounts of Snorre Sturlasson are considered to be pretty reliable. Maybe not in 100% detail when it comes to conversation or small heroic acts. But most of the persons, years and locations are backed up with archeological evidence and/or other written accounts. So if you could elaborate and give some specifics I may help.