I'm wondering what is the harm if a waiter/waitress was talking and happened to get their spit from talking into a drink?

Harm is unlikely: While spit contains a number of potentially nasty organisms, there are many reasons it would be unlikely to be of harm. It is diluted in a drink and especially if the drink contains alcohol, that will neutralize most harmful organisms. Next stop is the stomach, highly acid and able to kill almost anything else. The only thing that might escape all of this would be tb.