I'm editing someone else's footage of a lecture. The speaker is hard to hear if I raise the gain in the timeline every once in awhile the audio meter goes into the red. I read that its better to use the AU Dynamic Processor audio filter, but the only thing that makes it louder is raising the "master gain" which seems to have the same results as raising the gain in the timeline causing the meter to go into the red.

Note, my goal to better hear the person without creating painful sounding distortion when it goes into the red for brief seconds. I also have a basic understanding of compression and limiting but they don't seem to as intuitive in fcp filters as they are in a stand alone audio editing program such as Soundtrack Pro.

I know its bad to go into the red but what sort of effect will it have when exported to a DVD and played on a TV?

Use the FCP audio compression filter and change ratio from the default of 1 to 2. Adjust the db from -40 to whatever seems to do the job, -20, -15db, whatever. See whether the gain filter should be first or after the compressor filter. I would try the compression filter after.