^ One (possibly apocryhal) story that I heard was that Walter Koenig encouraged the extras playing the journalists to refer to him as 'Captain Chekov' in their adlibbed chatter during the scene where the TOS trio first walk into the Ent-B bridge, but it got picked up by somebody when they were watching the dailies and it was wiped out in the sound looping session afterwards. Whatever the case, Chekov clearly isn't wearing the rank.
Damn, his behavior on Enterprise-B was a good for him, but it's clear he was acting so McCoyish. Oh, and as we can see in The Deadly Years, having a higher rank than Captain doesn't mean you're good to command a starship. I don't think the Ceti Alpha incident would have get him a black mark on Starfleet files. It's surely noted that he's a desaster as historian, but it's not his own fault if this system had not been pointed out as having Khan somehere.
Kirk managed to get his ship hijacked several times a year and made admiral. I don't think Starfleet is too picky.