Even if you wash your coffee pot thoroughly after each use, you eventually still end up with coffee stains inside the pot.
Here is a good recipe to clean them:
1) Start with a cool pot (never clean the pot when it is still warm)
2) Add 5 Teaspoons of Salt
3) Add 1 Cup Crushed Ice
4) Add 1 Tablespoon of water
5) Swirl the ingredients together in the pot.