If your server is engaging in clearly unsanitary behaviors
If you just watched your server cough into your food, get the manager. If your server clearly hasn’t bathed in several days and their uniform is covered in so many unidentifiable, unspeakable stains that they look like they’ve just come from the bad sort of adult film set, get the manager. If you just watched them drop someone’s food, then pick it up off the floor and put it right back on the plate, get the manager. If your server cannot stop loudly farting while you’re trying to tell them your order… maybe don’t get the manager because that is goddamned hilarious, but if they smell like burnt hair mixed with Dick Butkus’s jockstrap, yeah, go for it. You get the idea.
If your server is on heavy amounts of drugs
This is a very specialized instance, but it does happen. Look, the use of illicit substances is pretty common within the restaurant industry -- less nefarious ones like weed and alcohol, sure (and if your server is stoned, it’s more likely to be hilarious than anything), but also heavier stuff. This is most likely to be cocaine (in which case your server might honestly be more attentive and productive than usual), but if they’re clearly tweaking to the point where they might pose a danger to themselves or others, it’s time to get the manager involved!
Most likely, “I think my server might be on heavy drugs” isn’t going to get a shocked reaction -- the boss probably knew, but they had 100 covers and five servers all night, and no one else could make it in, so they just decided to roll the dice. The fact this happens is perhaps an indictment of the restaurant industry itself, but there are so many things to serve as indictments of restaurant industry practices at this point that it’s relatively low on the list.
If your server has been openly racist, creepy, and/or threatening
This is a very uncommon one in most places. Our income depends on making customers like us, even the racist servers (and there’s no shortage of those) are good at hiding it, and most servers aren’t stupid enough to make a customer actually feel like we’re going to punch them even if we really, really want to. But it does occasionally happen. If at any point your server has made you feel unsafe or clearly crossed any lines, ask to speak to someone in charge immediately (maybe by asking another server if you’re worried your own might put an oyster fork through your kidneys if you bring it up with them). Bottom line: you should never have to feel uncomfortable or unsafe during your restaurant experience.
If your server was especially great and you want to give them a shout-out
This is the big one that doesn't happen nearly enough: if your server was particularly good, don’t hesitate to ask to speak to a manager in order to sing their praises. You’ll probably get an instant look of terror from the server when you ask, but keep going. If the manager is nice, you’ve just made your server look good. If (as is more likely) they’re a dick, then you’ve just handed your server a card to play against them if they ever try to step. Either way, your server wins.