I used to know that, but forgot.
They are strictly text and yes/no TVs, but things have just gotten extremely weird. I'm now getting that same error in the Manager when I try to edit them and Quick Edit fails silently.
This is only happening with the TVs for a particular extra (of mine), so there must be something wrong with the way they're being created.
[Update]I think I see what it is. In the 'properties' field the problem TVs have array() instead of a:0:{}
[Further Update] I'm a moron:
'properties' => 'array()',
The extra is at least a year old and has always worked fine. I've had E_NOTICE on in my development environment for a long time, but I must have released the extra before it got turned on.
Never mind.