Feature flags are essentially identical to operating A/B tests in this respect, right? I have a magic button which logs me in as a target user, and it reproduces exactly what they would see, including the results of A/B tests. This helps to reproduce unanticipated interactions between tests. (This has only happened maybe twice, but they were doozies.)
Not really. You just add extra tests for your new functionality as usual. If you're replacing old functionality, you'll have duplicated tests until the feature is rolled out for everyone.
I think the key is being able to tell if bug reports are related to an activated feature. For instance, our error tracker tells us which user account triggered the error. From there, we can see what new features they have enabled, and factor that into our debugging.