Geez, I've never had any of these issues. Some years I've had a different tire on there, but other years, no. Maybe I am not working hard enough?
The only damage we've had was to my DH's shin when he fell backwards off the stability ball and his leg got attacked by the chain ring on my bike on the trainer. He still has the scar, 8 years later.
It was kind of comical to watch that because he could have stood up after falling off the ball, but instead, he flopped over and hit the bike.