Facebook has had a big week. The social network finally caught up to MySpace in the U.S., according to ComScore. News leaked of its upcoming Everyone button. And Facebook made some significant improvements to its search capabilities. Now the social network is improving its inbox’s interface, which previously was a little clunky and difficult to organize.

The new design gives you filter options at the top of your inbox to help you identify unread messages as well as to report any spam, or unwanted messages you receive.

Facebook has also ramped up its search feature within the inbox, which was lacking in its earlier version. To find specific messages, you can type a keyword or a friend’s name in the search box in the upper-left corner of the screen, and then the results come back only for messages from that person. Yes, this is pretty basic stuff, but it should make it easier to search your Facebook inbox.

Facebook is keeping some of the same functionality as before. You can still view Updates from the Facebook Pages you are connected with. You can also manage subscriptions to your fan pages by clicking the “Edit Subscriptions” link beneath “Inbox of Updates.” Facebook says it plans to send messages from Groups and Events to Updates as well.

Friendfeed has also updated its email capabilities today, making a few useful improvements its email alerts for new subscribers.