Some great answers here and a lot of my thoughts are already covered. Besides a lot of the good points, I think it boils down to these:
1) Are they good at what they do (strategic + creative)?
2) Are they easy to work with (chemistry)?
3) Do they come through on their promises (meeting deadlines + deliverables)?
I would also ask about their print vs. digital background and experience. Since we live in a digital age, some firms offer print capabilities but really without the background or experience dealing with print projects. The same can be said about digital.
Some folks mention process and that is good to know because a process can help define expectations and check points. Know what is expected from them at what mile stones and also what is expected from you as a client at what mile stones.
Some firms nickel and dime you on everything. Be sure to understand what is covered and what is not in the contract. We do everything on a project-basis and deliver the end product no matter what it takes as long there is nothing that is a change of direction or outside of the original scope. The client understands what they are paying for and at the end, they get a great product, not an invoice with extra stuff here and there.