I would be surprised if the disc were dirty, but that is an easy thing to try. The disc is housed in a closed drive so more than likely it is pristine. I have the same problem with our 2004, however, that occurs and random times and not just when starting out. I believe a more likely cause is the drive itself. Likely the drive is starting to fail, but it does seem like a very slow death. This has been going on for over a year for us but isn't bad enough for me to change out the drive. However, the problem has only gotten worse (albeit slowly) so eventually I expect the drive to simply die.
2013 Audi Q7 S Line Prestige (incoming)
2005 C6 Vert Silver/Red
2004 MDX Silver/Quartz (T/N) -- being traded
2009 Honda Rebel