Is there an easy section to cut out one piece of a baseboard?
You CAN remove a section and patch, but the effort involved might make it work replacing the entire length.
First off, given that it is a 15' span, chances are it is two pieces scarffed together.
If you chose to try to replace, tools and supplies to consider are a multi-cutting tool - something similar to http://www.harborfreight.com/multifu...ool-67256.html. Cut out the offending piece, cut a piece to fit and use drywall mud to fill. I have found this to be an extremely effective method of filling painted moldings. Really good on crown. Pick up some 20 minute mud at the local store, mix and apply. Wait the 20 minutes, sand the finish, primer (VERY important) and paint. Should look seamless.