The Save Edits dialogue would be a lot more useful if it allowed for deselecting one or more feature classes. Thus not saving those (could be saved later?).
When editing some edits may have ended up in the wrong - not the intended target - feature class. If you happen across this situation there is no elegant way out. Either you lose (do not save) any of the edits or you accept some incorrect edits to a non-target fc.
Suggest to add a check-box behind the names of listed FC, so a user can deselect an FC from that save. The edits from that unsaved FC can be continued and saved later or discarded at a later stage.
Alternative: have a dropbox with three options: save, do not save (keep edits), discard (edits).