There are various ways to find out which projects, clients, activities, and other items are not a part of groups or have no group assignments.
If you go to the Productivity Tools menu > Groups, click More > View Reports. Select the Groups report as it lists all the different groups you have created in Core and there is a 'drill through' option to see who is in each group. If you have a list of projects that should be in each group, you can narrow it down by the process of elimination.
Another way is to open a group's detail view from the Groups screen and click Action > Assign Project. In the assign view, choose the 'Unassigned Projects' to get a list of all projects that are not part of this group. You will have to check the detail view of each group the same way.
A third option is to run the Groups report filtered by project that can be accessed from the Reports screen. It lists all groups with individual projects. The Document Map section shows all projects under each group. Please note that the View Document Map option on the toolbar of the Viewer is turned off by default and needs to be turned on to see the left panel.