That's bizzare. I haven't seen this in testing, and I've added A LOT of players, so something is not configured correctly ...
(0. By the taxonomy file I meant taxonomy-teams.php.)
1. What version of WordPress are you running?
2. Please send me a screenshot of the main Edit Players page.
3. It might be worth DELETING the plugin and re-installing a fresh copy. You might also install it manually using FTP rather than the auto-install feature. You should not lose any player data but you WILL lose and changes you've made to the plugin stylesheet, so move that to a save location first, then write it back over the plugin's base version.
4. You might try loading a roster from a CSV file and see if the same problems occur.
5. Turn on WP_DEBUG and see what errors come up on the admin screens. (You can find out how to do this by Googling it.)
6. There may be a plugin conflict (although I doubt it). You can check by deactivating (don't delete, just deactivate) all other plugins and see what happens. If everything looks good, you can re-activate the plugins one and a time and see when/where you get a conflict.
Interesting. We'll figure it out.