Each release has its own changelog page, in which the possible breaking changes are notified.
When installing a new version, it's important to review this list and see if your projects are likely to be broken by those changes or not.
A safe thing to do is to make backups of your projects/capx before opening them in a new version and to save them as a new project/file from within C2.
As far as features go, well a new feature may contain bugs, that's the purpose of betas. Depending on the feature it may or may not act on the "core" of the soft, but generally it doesn't.
For example, r115 is mainly a new export option, so the rest of the soft is untouched.
I'm always keeping to the latest beta and it's been pretty good so far.
Some versions had "major" bugs that made projects not workable anymore. When this happens, Ashley generally release a .2 in the couple of days following the first report of such issue.
If you want to be safe, don't download the beta on the very time it's released, wait a couple of days to see if people will report a major bug or not.
Anyway, you can install multiple instances of C2 (for example, a stable on the harddrive and beta on a USB key).
There are always ways to get back a corrupted project saved in a beta version to an older stable release (as long as the project does not use specific features only available in the newest beta).
It's "hacky" but it's possible.
Lastly, if you're looking to export and upload a game to Scirra's arcade, you are to export it in the latest version of C2 anyway.