In particular, the code for submitting a choice does not use group mode when determining whether the maximum number of choices has been reached. If a choice is limited to 1 it will prevent you from choosing it if 1 person has already chosen it - even if they are in a totally different group.
The form that shows you options does already work correctly, showing that the choice is 'full' if you select the group where somebody chose it, and showing it as available if you select another group.
This is critical for a usage in a course here where they want people in each tutor group to pick a subject area for projects (the idea is that everyone in the group does a different part of the issue, so with the whole group together they cover it, I think). As there are hundreds of tutor groups it is a bit of a problem if only one person in one of those groups can choose the option.
(Wow, choice module is horrific. I do not intend to fix general suckage only this specific issue!)