I don’t think the Han/Greedo scene ruins Han’s character since it’s not like Han is waiting around for Greedo to shoot before he even considers shooting. Instead, Han shoots only a split second after Greedo, which shows that his self-preserving instincts are still intact from the original version.
That being said, it is still a very stupid scene because Han’s instincts were too slow and it’s ultimately luck that saves him (Greedo missing) rather than his aforementioned instincts. So it ends up being a stupid-looking change with an awkward head dodge (that wasn’t even necessary since Greedo’s shot was still wide) with no real impact on Han’s character other than learning that luck saves him more than his instincts.
For me though, the worst SE change is Vader’s “Noooooo!” in ROTJ. It completely ruins the film’s climax and injects unintentional humor into what was previously an emotional moment.