Something that immediately jumped to my mind is bettas getting stuck in terracotta pots (or whatever else) and ripping their scales off/drowning. I've seen some very sad threads on here about that.
Here's a thread about a betta that buried himself and drowned, and Myates has a good quote there for your purposes.
"Poor guy.. I have one that needs to be in a bare bottom tank as he will always get stuck under and in between things. Almost daily I had to rescue him.. silly fish. Good thing you got to him in time, as they can drown."
Also, tailbiting! Such an absolute nightmare to address and fix sometimes.
I haven't had many personal issues... I've lucked out with my bettas. Sky started tailbiting, but stopped when I moved him to college with me. He can see me all the time now and that seems to make him happy. I've had him over a year, and now that he gets a ton of interaction, his personality has completely changed. He's much more active and I can't believe how colorful he is now! Bettas are so much more beautiful with attention and effort.
Also the bettas that jump out of their tanks and die that way...