Sumiki got the closest answer, so he's this week's winner!

Answer: The German spies wore identical hats with secret information hidden inside the hatband. They entered the restaurant at slightly different times and placed their hats on the hatrack where they would see them. They left at different times -- each taking the other's hat.

Rules:

1. Don't share answers with each other, even answers you know aren't right. Doing so will get you disqualified for that round. This also applies for stealing another person's answer when you didn't come up with it yourself.
2. You may, however, share theories. If you come up with an answer with the help of another contestant, make sure you mention that you did so, and who that was so I can give them credit.
3. Each round, I will post the clues that correspond with that puzzle in a spoiler tag, assuming there are clues. Yes, there are some with no clues. Deal with it.
4. If you have heard some of these puzzles before (Rockhound and Robo, I'm looking at you), out of courtasy to the other contestants please don't share the answer to others.
5. There are no prizes for winning, save bragging rights.
6. If you believe you have the answer, post it in spoilers in the comments. Share theories through IM, PM, whatever floats your boat.
7. You will have one week from the posting of the new puzzle to solve it. Afterwards, the blog entry will be locked.

Clues:

Go!