We have agreed we can veto someone early on if we get a really bad feeling about somebody - I know sometimes people get giddy over somebody new and don't really see things that could be problems. That is why we prefer to meet people the other is dating fairly soon, I don't think its fair to the third party to try be able to pull the plug whenever.
I don't picture using it - my husband hasn't dated crazy needy dysfunctional women for a long time, and I have only seen him date sane ones since we have been together, most of whom I have liked.
We do have veto in another way I suppose. We don't have hard and fast rules about dating somebody based on their sexual activities, lifestyle, or dating style (some things really just aren't our thing but we don't have a "you can't date somebody who does that" clause preset up because each person is an individual), but it is possible that we realize after awhile that we aren't going to be comfortable with that third person's choices. I have found some of that information just doesn't come up in the first few dates, and decisions might be made a bit later down the line.
I imagine that (working hard to come up with an example I would actually want to veto) if somebody my husband was dating for awhile started having unprotected casual sex now and then, got into risky blood play & started phoning at 2 am wanting to chat because she was feeling insecure - well he probably would've already broken up with her, but I imagine in that case I would be sitting him down at some point if there were ongoing issues and saying I didn't want this person in his life as a girlfriend anymore.
Admittedly if somebody he dated cheated on say - their primary partner, he might be more tolerant because he just is and knows people make mistakes - but I might ask to veto that person at that point because of a lot of personal reasons and history. Hmm that makes good conversation fodder for tonight.