Might not be the right sub.
Specifically I'm fascinated by the ending bit where Tony reveals that Factory Records never had binding contracts with their artists. Is that true? How did he get away with it for so long?
Also, pretty much everything to do with Happy Mondays' fourth album. Did they really fuck up that bad? Did guns get involved?
It is true that Factory didn't have the rights to their artist back catalogs. Or at least some of their artists, most famously, New Order. So yes, that part of the movie is factually correct.
As for the Barbados recording session of Yes, Please! Yes, it was a fucking disaster. The events as described in the movie are widely considered accurate.
I think the gun is more legend as I can't find a first person account of it. For more I would suggest Shaun Ryder's autobiography Twisting My Melon.