I generally prefer to watch the show "blind" but I did stumble on the Ash-identity theory (probably on this very forum!) early in the show's run. And something that has always bothered me is the origin of Ash's backstory as discussed by him and Lorca in their chat while training on Klingon-shootin' in the disco-holodeck.
As a Seattle native, that conversation stuck with me :)
Presumably Lorca got Ash's background info from Starfleet personnel records, which means either: 1. L'Rell's house of spies managed to implant a fake Ash record in the Starfleet database, or 2. Ash Tyler was a real person who was captured by the Klingons and replaced. I would assume #2 is more plausible, but it seems odd that they wouldn't have mentioned "oh you're the guy who went missing" or something.
Any other possibilities I'm missing?