Yes, there are usually azimuth issues with auto-reverse decks be it slight or heavy.
Then there's the Nak RX-202 that solved that problem. It is one of the best auto-reverse decks ever made in my opinion. Not only does it solve any azimuth issues by flipping the entire cassette over, but you get to watch the show as well (provided you don't blink).
IT's also one of the best sounding 2-head decks ever. I use mine for playback only and have not tried recording on it, so I can't speak to that, but I hear it's a good recorder.
Then there's the Nak RX-202 that solved that problem. It is one of the best auto-reverse decks ever made in my opinion. Not only does it solve any azimuth issues by flipping the entire cassette over, but you get to watch the show as well (provided you don't blink).