I reject a case for: A split body, split neck, any vertical mark on the neck or body that might be a split in the making, any dent if pistol brass, a large dent if rifle brass, a messed up rim if pistol brass, a messed up rim that a file can't fix if rifle brass, incipient head separation, a squished case mouth on pistol brass, a most horribly squished case mouth on rifle brass, and any scratches or scrapes that are not shallow.
Out-of-round case necks are fine... sizing heals all wounds. Even a badly squished case neck on a rifle round can be carefully opened and then sized into shape with no harm done, so long as the brass isn't actually scored or split.
I don't worry about the rims, as they're easily discovered during normal processing, nor do I think they're a safety issue so long as the base and body of the case are in good shape. Messed up pistol rims are invariably discovered when the round won't go all the way into the max cartridge gauge I use before I box the round. For rifle brass, if I didn't notice a bad rim during lubing, I'll notice when it won't go smoothly into the shell holder during trimming.
Oh, tools? A tumbler full of walnut and maybe some Nu-Finish car polish.