Generally speaking I've been happy with Doggcatcher's behavior with Android Auto but I've noticed a couple of issues:
Sometimes when I click to start the app I'm left in the list of audio playlists with no way that I've found to just get the app to resume playing what it was playing before. I have to pick up the phone, open the app, and then click on the "Play" button on the phone screen. This problem doesn't seem to always happen--in some cases the list of audio playlists shown in the Android Auto context has a "Play" button on the right-hand side.
In the main "What's playing" screen the time freezes and the completion "bar" (i.e., circle) freeze. If I click the "Pause/Play" button (twice), both start advancing again.