This is a movie that's more "interesting" than it is "good". Orson Welles made it by reusing a couple of scripts from his extremely entertaining radio series The Lives of Harry Lime, but it doesn't really hold together. Or make sense.
I'm pretty sure I understood the plot, which involved the titular Mr. Arkadin (Orson Welles in an extremely silly beard and even sillier accent) hiring a guy to dig into his past, claiming that he has amnesia and wants to know where he came from. It's really just an excuse for various disreputable and colorful characters to tell stories about Arkadin's youth. If i had worked, it would have been like a seedy version of Citizen Kane, but it doesn't fly.
I watched the Criterion version, which has several different edits of the movie. Apparently Welles didn't get final cut, so the studio released a version that he despised. The Criterion version has three or four different cuts, but I don't think it makes any difference. It's an interesting failure, but that's still a failure.
One thing did interest me. There are a lot of scenes that involve a lot of chatting and expositioning, so the characters keep moving around to keep the scene visually interesting. It looks pretty tiring if you ask me, the way they keep circling each other like that. There's a boat scene in particular where the characters are flinging themselves back and forth like the Enterprise is under attack by Romulans.