Question: I'm working on a browser add-on that has some novel usability ideas, and I'd like to test them out on some users. The add-on interacts with the user's password data and usage, and I'd like to collect some (non-identifying or exploitable) data. In particular, I'd like to keep track of how many passwords a user has, the average number of sites they're used on, the number of characters in each password, etc.

I realize that I'm treading on potentially shaky ground here. Where could I find users interested in testing such an add-on? How can I assure them that it's safe?

Other than open sourcing the code, which I'm already planning to do.

Answer: 
"Where could I find users interested in testing such an add-on?"

Moms. Church secretaries. The pointy haired boss. Basically anyone that would be naive enough to install a browser plugin that tracks their passwords. These people are also a direct correlation to the people's machine's I need to wipe clean and reinstall the OS every holiday when I see them. ;)

And, realistically, I doubt those are your target demographic anyways. I think open source is the only viable way to go. Hopefully some security-aware developers or the like will trust the software enough to help out with testing.
Well an alternative approach would be to look at students who would be interested in keeping track of the numerous passwords they have .They are generally tech savvy and you would be able to get considerable user feedback about potential bugs or concerns