In fairness, the radio message was a little indistinct, and the film version is what has effectively become history.
Lovell’s said in interviews that yes, there was a brief bickerfest, fueled by cold, hunger, frustration, and fear, but out of respect to his friends he wouldn’t describe it. Ron Howard and the actors worked the scene out themselves for the movie.
You may be right about the other items you list, but they’re completely forgivable even if true. One thing I do recall from Lovell’s interviews was that the mockup CM instrument panel had one light the wrong color, but otherwise the props people nailed it.
Some of the lesser characters, like the controllers in Houston and the reporters, were composites. Mattingly’s role in working out the checklist was not central. The jury-rigged scrubber wasn’t designed via a box of parts dumped on a table; the chief scrubber engineer worked it out in his head while driving in and the team just wrote the instructions. But again, so what, really?
But yes, it’s one of the greatest movies ever made, because it was one of the greatest stories ever to really happen. Let me strongly recommend Lovell’s autobiography Lost Moon (rereleased under the title Apollo 13), which was the primary source material for the screenplay, and has much more detail. That episode of Hanks’ HBO series From the Earth to the Moon, which if you haven’t seen you must, was about what happened on the ground - there was no point in remaking the movie.