The problem is metadata and isn't confined to Scrivener. iWork 05-08 files also have problems, although there's no problem with iWork 09. Here is their current warning:
If you use multiple computers, it is possible that putting these types of files in your Dropbox and renaming or editing them could cause them to break when accessed from other Dropbox-linked computers. The Dropbox engineering team is working on backwards-compatibility for files with metadata. In the meantime, you should avoid storing these file types on Dropbox until the problem is addressed.
There is a fix that's been in their pipeline since February 2010 and is being tested. If you consider yourself a "brave soul," you might want to join the project. It'd be particularly helpful to make sure the fixes in general work well with Scrivener. Use Scrivener's backup feature consistently, and you wouldn't be at risk of lost files.
Good news everyone: There is a new version of Dropbox that supports these kinds of files in the Dropbox forums. The Forum's version is an an early release for brave souls willing to help test new versions of Dropbox. If this applies to you, make a backup of your Dropbox folder before upgrading to be on the safe side. See the forums for more information on what is included in the new release.
I'll be absolutely delighted when this fix leaves beta. Currently, I do all my Scrivener writing on my MacBook because the hassle of risk-free synching it with my iMac is just too great. TaskPaper and WriteRoom synching via SimpleText have taught me the joys of multi-platform synching. I'd like to spread that joy to Scrivener.
--Michael W. Perry, Untangling Tolkien