For example, Dave would just need to search for "in:important" to get all items labeled "important," and Adam would just search for "is:unread in:inbox" to see all the unread messages in his inbox.
Here are a few other useful ways to filter your inbox:
We've written about search operators here before, but lots of people find them hard to remember. That's why we built Search Autocomplete in Gmail Labs, designed to make searching in Gmail much easier. Instead of having to remember the exact syntax for advanced searches, you can just start typing, and search autocomplete will help you fill in the rest. If you find yourself doing some of the same searches over and over again, consider creating a permanent link to them using Quick Links in Labs.