Chats
A lot of the time, when I talk with new people, they are actually surprised we have chats on this site - I expect there is a lot of people who do not know it after long time of using the site.
And since we want a community, which forms best when we can socialize, it is in our best interest to make sure people know about chats, and know fast. I know we have magical find chats but we also know hat search syntax is one of hardest things on the site right now. This filter would be then aimed mostly at new people and for convenience of others.
Ads and/or Ideas
Currently there is no way to browse just advertisements, from what I have seen - at least no syntax is revealed that allows for it, and my trying to find them did not help. Adding something that would show only not-started RPs. Since Ideas are almost the same, I think something like that would help as well.
General idea here is to make sure that it is easy to filter only for the roleplays you can actually join when you go through that part of the site - more convenient way than having to filter them manually or go through profiles and see if they have Ads/Ideas.
Finished
A filter that would only show finished roleplays for people who want to go around and read, not exactly play at the moment - since we emphasize showing one's skills by having public roleplays, it would be, again, nice to be able to see them from roleplays, not by jumping around profiles and seeing if they have any.
Would also increase chance of being approached for a play, given somebody can find your roleplay and only thanks to it become interested - not by finding specifically you and then checking RPs to see if you are a good partner. More options == convenience.
Probably could be later used if we went with some of the suggestions that would allow to vote-up well-written RPs