This could be an easy fix. First try repainting the spots. It's possible that they need a little more paint.
If this doesn't work, purchase a spray can of Kilz Shellac and reprime the spots. Apply 2 coats of shellac with 30 minutes of dry time between the coats. Allow the primer to dry for 1 hour then touch-up the spots. Two coats of paint might be needed over the primer, this depends on the quality of paint you are using. Allow 4-6 hours for dying between each coat of paint.