Whenever my phone attempts to play any notification sound (new text message or new email), the sound is not heard if BeyondPod is playing. However, the sound from the podcast dips to silence and then ramps back up. This means that:

  1. Notifications are often missed.
  2. Parts of podcast are missed.

  1. Play the notifications sounds (and put in an option to adjust that behavior).
  2. Rewind the playback by two seconds and replay (without dipping the audio).

Audible.com's Android app handles Android notification sounds the way I just described, so it is apparently technically possible.