As in any social gathering, people are likely to congregate into certain groups during the event. Some may give their token greetings to all in attendance, but as it progresses, some of these people are naturally going to gravitate together. Here's a half-dozen ideas to run with...
1) Several of the older affluent men head to a side room, a far corner or even outside to enjoy a quieter atmosphere. They light pipes, pour some drinks and begin telling their worn-out tales of past glory. They'll happily keep talking to anyone that will listen. Unfortunately, a couple of them get into a dispute over the facts of who did what during a minor battle years ago. If the party doesn't get involved in calming things down, it escalates to a full duel. One individual is right, and the other is mistaken, but figuring out which is which without causing a big scene will take skill.
2) A very attractive foreign merchant (to this city at least) dances with many of the girls who take a big interest in him. As he dances with each of them he secretly asks many of them to meet him by the stables afterwards, telling them they are his newfound love. He chooses girls who seem unattached to anyone. He's actually a slaver. With the help of his guards, he winds up capturing the girls as they enter the stables, gagging and binding them, then loading them into his wagon in large crates. He immediately heads off to a nearby port to ship them off. The missing women may go unnoticed until the morning.
3) Several of the younger men get together and stage a drinking contest amongst themselves. Anyone is free to join. Afterwards, these drunkards wind up causing all kinds of problems at the ball, getting overly loud, being offensive and so forth. Unfortunately, one of them is considered to be royalty, so kicking them out of the ball is no easy task. The party can try to find an alternate way to make them leave, but they'll need to think it up.
4) A couple of the younger men involved in the drinking contest slip off and decide they must do something completely over-the-top at this ball to impress a couple of the ladies they've got their eye on. Of course, they are pretty drunk, so they come up with an ill-conceived plan of saving the ball from a fire breaking out in the kitchens. One of them lures the cooks outside and the other starts a major grease fire. The fire spreads more quickly than expected and his attempts to douse the fire by dropping a large barrel of water on it has disastrous results, as the grease flies everywhere. Soon the entire kitchen is ablaze. The party will need to work quickly to keep it contained.
If the party is successful, they turn out to be the real heroes. The ones who started the fire attempt to slip out of the party, hoping that no one notices them. If asked, one of the cooks may be able to identify them as "acting suspicious" before the fire broke out. The 2 ladies they were trying to impress wind up falling for the partymembers instead.
5) Two slightly drunk women begin yelling at each other about a missing bracelet, with one claiming the other has stolen her precious and valuable heirloom. Eventually it turns into a full-blown catfight, and many of the drunken males even spur them on. Unless the party moves to intervene, the two ladies claw and scratch at each other and by the end their clothing has been reduced to scraps laying around them, leaving the women exposed to the entire crowd. Unless the party acts before this, a pair of men finally pull them apart and drape them in cloaks. They continue their yelling, but then calm down, finally becoming fully aware of their nakedness and greatly embarassed at the fact everyone witnessed this. The actual bracelet was stolen, but by a male thief at the ball. In fact, he's lifted a few other articles from guests that have so far gone unnoticed. If he's caught, those two women from the original fight now turn their wrath upon him unless they are stopped somehow. Given the opportunity, they take their vengeance by tearing off the theive's clothing and in the process revealing all the stolen items. He attempts to flee, but is easily captured by the guards.
6) A rather unattractive wizard seems to have caught the eye of a beautiful lady at the ball and they spend much of the time together at the dance. Her fiance is concerned that the wizard has cast a charm on her, and wants the party to investigate. DM can run this one of two ways. EIther the wizard has charmed the girl, or he hasn't. To explain the latter, it's possible that the wizard is actually some long lost friend.