Right now the group is contained in the path of the bookmarktrail. This means that it is not possible to have a sitewide bookmarklet and it also causes a bug where you can submit a solution in a different group than it's problem (e.g. if the last problem you visited is in another group).
1 way to solve this is remove the group from the path in the automatically generated bookmarklet and use instead the group from the last visited problem to prepopulate the form when submitting a solution. You might also consider adding a JS tweak that will change the group if the referenced problem is changed.
The other option is to keep problems (that contain the confidential information) bound to a group but to make solutions site wide, but then any member of your site will be able to see all solutions (which might still give hints of the type of problem you are trying to solve).
What do others think?