Ok, it's looking like the following fields will not be allowed in Field Groups.
Editor Text Area
Image
File
Video
Audio
Rating
Points
The reason the above won't be allowed, initially, is due to their jQuery bindings not supporting being rebound when CB Repeat clones them. The plan is to fix that behavior in CB it self when possible and then enable those fieldtypes in CB Field Groups. Additionally the following fieldtypes will never be permitted for grouping due to their intended function and behavior.
Gallery
Activity
Comments
Notifications
Follow
Like
Privacy
Progress
Forum Status
All other field types will function fine and as intended. For example Text, Text Area, Integer, Email Address, etc..