This is what would have helped me in this particular incident:
Let me see deleted messages in chat just like I'd see deleted questions or answers. Show them with a reddish background and let me toggle all, or some of them to go away. I had to load the transcript more than a few times, and I use TCP over carrier pigeon (@Waffles will attest to that)
Give me access to all moderator tools by clicking a user's gravatar. To avoid fat fingers, perhaps open those tools in a suitably sized modal dialog (similar to the moderation tools on the parent sites) from the menu a gravatar click produces. IOW, let me deal with disruptive people without taking my eyes off the room. I realize some tools do require another page load, but let me do as much as possible in a modal.
Give me a flag summary (as @Shog9 suggested)
Organize chat flags with some kind of sorting and pagination. It's extremely typical for there to be enough flags that the dialog to deal with them becomes obnoxious.
Addendum regarding sock puppets:
Content in chat is, by way of comparison with the parent site ephermal. While it would be nice to have tools to figure out if someone was circumventing a suspension more quickly, I wonder if keeping them out in the first place could not be a little more automatic. If detected that the probability of an account being a sock reaches a certain threshold, don't let them in. Let a moderator review it. They're attempting to type in a chat room, not contribute to the parent site.
Now, for some chat 'policy' that we might want to consider:
If your chat room is not in English, you have no hope for moderation. If your room generates too much non actionable noise, a moderator will likely shut it down. A substantial amount of flags that I see (and I'm one of the more active moderators in chat) are in a language that I can't understand, and poorly written enough to confuse tools like Google Translate. I don't want to force people that speak a common language not to use it, but we can't be expected to render assistance when we have no context. If your room does nothing but create work for people that are otherwise using the system as intended, your room needs to go away.
I fully support an additional barrier to create rooms, as suggested by @Ninefingers
I really like our chat system, in fact I wish I could use it at work because it would solve so many problems. But it does seem like moderation was welded on as a bit of an afterthought ... probably because it was built by people that naturally behave constructively.
If we could make the tools resemble the tools on the parent site a little more, moderators would be more effective at repelling those who want to make sure that we can't have nice things :)