I notice that Stefan's question has not been answered.
My client wants the redirect after saving the profile, in the edit profile screen to not redirect to the profile viewer.
This is exactly the same question as Stefan's.
After hours of research and trial and error testing, I found the following solution:
In the file /components/com_comprofiler/comprofiler.php change the line:
cbRedirectToProfile( $uid, CBTxt::Th( 'USER_DETAILS_SAVE', 'Your settings have been saved.' ) );
to the line:
cbRedirect("index.php?option=com_comprofiler&view=userdetails", CBTxt::Th( 'USER_DETAILS_SAVE', 'Your settings have been saved.' ) );
That makes it redirect back to the Edit Profile screen instead of attempting to redirect to the Profile Viewer screen, after saving the altered profile.
Of course, you always have to take care in case a future CB update overwrites the hack, in which case you will have to re-apply it.