Who ever that someone was they got it right. For the sections that need another coat you will need to use the same application method, example- use a paint roller. This will minimize any flashing that could happen. If the sections are very large plan on painting from corner to corner.
If the scuff marks return after touch-up then you will need a stain blocking primer. There some in spray cans that do work, both Kilz and Zinsser Cover Stain are great for this type of job.