This is great and something Dropbox should do. This would make for great PR. The QR code idea underneath my post would be great on the back. Just a huge QR code.
after thinking about how to actually make the shirts, how much more per shirt would it cost(considering each QR code would be unique)?
The Dropbox shirts comes with a TOS that they own the cotton.
how about just a QR code on the back to a sign-up page with the shirt-wearers referral code?