Unfortunately, there is little solution for this problem. You can call a cab for them and send them on their merry way, if you're comfortable that they won't be sick at home alone. You can guide them to a bedroom if there is one free at the location and get them a cup of tea and turn out the lights, but if it's not your house, this doesn't really work. And often, they will pop back up in half an hour ready for round 2. Definitely cut them off and only serve them coffee if thats appropriate.
I think its a good ssign that this guy was embarrassed at his bad behaviour - its a sign that its slightly less habitual - and just talk to him about his behavior and reccommend the guy go easy on the booze for awhile. But this honestly sounds like maybe the guy wasn't clued in to appropriate behavior? I know a lot of guys dont understand the whole tarts and mimosas aspect of "showers" and maybe he thought it was just a party. (still speaks to a problem with alcohol, but maybe he wasn't so much rude as clueless).

How about, be an adult and make sure your friends aren't being over-served to begin with?

Just ask him to leave?

Re ebarrett3's comment: I didn't realize that it was the host/hostess's responsibility to police every single guest to ensure they haven't had one too many. I would like to assume that the friends I would invite to a party are adults who can be trusted to police themselves. Putting the onus on the person hosting the party is absolutely ridiculous.

Put him out when he gets obnoxious. Better to have five minutes of possible drama at the door, rather than your entire guest list having to deal with him for the rest of the night.

Since you decided on the cocktail party format, things like this may happen. I would identify the people that were offended and apologize to them specifically. For example, the women who had their bums pinched and the hostess. However, every adult has experienced situations like this in the past and would not likley hold his behavior against you. For future reference, if you are aware of guest's offensive behavior, let them know about it and ask them to correct it or leave. I agree with Lauraska, the idea that you need to supervise the alcohol intake of your guests is absurd. We should all act responsibly and this isn't this person's fault.

I don't think it's that simple, Joe. I am sure that she wasn't the only one serving drinks and that the rude guest had access to help himself. How about instead, he act like an adult, and take responsibility for knowing his limits? I would have told him to leave.

Wait wait wait, ebarrett, since when is it anyone's responsibility but YOUR OWN to police how much you drink? I'm assuming this was a serve your own drinks sort of affair and not something with a bartender who does have a responsibility not to serve an intoxicated person.

Really though, both are the same issue. The host needs to act like an adult and stand up when it is clear that an individual is making a number of people uncomfortable. The drunk party guest needs to behave like an adult and not get completely smashed.

Whomever invited or brought this person should be the one that gets them out of there. The party was for you and to celebrate this wonderful milestone in your life (Congrats!)
If you are hosting and your friends comment to you that they are uncomfortable (and sounds like a little harassed) by this person you need to say/do something. If you shrug it off, don't be surprised if they start to feel frustrated with you, too.
The next day remind the person of their behavior.. hopefully they'll feel bad. If they don't you might want to evaluate the value this person brings to your life.

Yeesh, i've seen people at many a college kegger handle this situation WAY BETTER, how embarrassing! Put the drunk in a cab and wave goodnight. What kind of friends are you inviting to your party that you feel too scared to go up and say "you're done, time to go home"? And speak with the host/ess next time instead of just ducking and dodging all night.

Yes, this is a job for the host/hostess, NOT the person of honor. So don't feel bad about it unless you forbid the hostess to do anything about him. Brides are expected to throw drunks out of their wedding - neither should a mother-to-be have to deal with the drunks at her shower.

One good way to deal with a drunken guest you can't send home is to get someone with a rather forceful personality to monopolize his attention and drag him off to a quieter corner of the party and ply him with food and water until the stupidity wears off.

Get rid of him before he gets that drunk.Put him in a cab or have someone take him home. If he drives and gets in an accident and you supplied all the booze you could be held responsible.

Film it, post it on YouTube/FB and let the blackmail ensue!

I'm with Kaete - it's not the guest of honor's responsibility, it's the hosts'. And regardless of whether the host is doing the serving and "responsible" for monitoring a guest's consumption, the host IS responsible for ensuring the safety (and, hopefully, good time) of all the other guests - which may mean the host has to address the consumption of someone who is not being responsible for himself: put him to bed, cut him off, ask him to leave, or BE the person to guard him to prevent his misbehavior with others. Part of hosting is accepting this role, even if it means not having any fun.

It sounds like the mother-to-be feels responsible because perhaps she put this guy on the guest list. It's thoughtful that she has apologized on his behalf - but he needs to do the apologizing, so maybe she can help make that happen.

I'm puzzled as to why this question needs to be asked. How do you get to the age of sensible cocktail parties without knowing how to handle someone that's had a few too many. Everyone gets a bit pissed and acts the fool sometimes. You can either enjoy their behaviour and see it as entertainment, and leave them to their devices, or discretely go over to them, tell them they're wrecked, and to slow their roll so to speak.

In some ways the host/hostess is responsible for the alcohol intake of their guests. If, for example, a host/hostess provides alcohol to a guest who then drives home under the influence that host/hostess is somewhat liable (or at least so I've been told). Socially however, the guests should be responsible for their own alcohol intake but there's one at every party that crosses the "appropriate level of inebriation" line. His inappropriate sexual advances were completely inexcusable, drunk or not and he should have been thrown out of the party immediately. I know you were trying to avoid drama, but I'm sure others noticed his behaviour so drama was already taking place.