The problems seem to all be related to headphone use. They don’t happen when headphones aren’t used. This was the clue to the root of the problem — actually two problems.
If you’ve experienced these issues, take a look at your headphone-jack. Do you see any little chips or scratches around it? That’s your problem.
The design of the HTC Sensation allows your headphones to constantly “touch” the cover. Eventually scratches or chips in the coating appear, which expose the underlying metal surface of the phone. When the metal of the headphones come into contact with the metal of the case, one of two scenarios plays out:
The phone interprets this as a command from a headset with built-in controls: play, pause, skip, back, or volume. Of course that’s not what you intended, so it’s an “unexpected audio anomaly”.
In the other case, the headset and/or phone simply “shorts” which causes another type of “unexpected audio anomaly”: cutting out, hiss, pop, etc.
The solution to both scenarios is simple: cover the exposed metal around the headset jack. Putting that solution into practice, however, is not so simple.
If your phone is under warranty, you should probably look into having it serviced or replaced. If it’s not under warranty, you may need to resort to either a Bluetooth headset, or covering the exposed metal with an “insulating membrane” (electrical tape comes to mind, but it doesn’t look very pretty).
At least now we know source of the problem.