LootHunter: Well, since Mudd is a con-man, he could somehow erase it. Also, remember that the whole information about "shroom drive" is top-secret (like Section 31 level) and doesn't last up to TOS. So it's quite probable that Kirk and others don't have a clue about history of USS Discovery, Mudd included.
The detail of the incident might be classified, but not everything. After all, the fact he's a dangerous killer, basically a psycho going by this episode, who almost took over a spaceship, is vital information for anyone who might encounter him.
johnnygoging: I hope this isn't the last we've seen of Harry Mudd. I've always liked the sort of aloof, goofy badass. it's not a thing you see too often, and, in a way it makes a certain sense, as why wouldn't people who are capable of great things or surprising you/upsets not have some eccentricities to them?
I think it's fun to watch. think it makes for good TV/film. I hope there's more of him.
I like the character, I even like the actor they chose to play him, even though he's too old, but I don't like the way the show is using him. Like everything in Discovery, it's too dark and violent. But I'd be totally on board if Mudd was to be the villain in another movie with the "Abrams" cast, this time done as a kind of heist movie perhaps, or something like 48 Hours in Spaaaaaace.