A lady friend of mine works part time at a chain restaurant, she says there trade secret of cleaning their "Bunn" pots, is salt, and ice cubes.....just need a couple.....to cover the bottom of the carafe, give it a good couple swishes, and it'll remove the coffee stains....
At home though, I just make it a habit to throw my pot in the dishwasher once a week or so, top rack only. Now if it's one of those thermal "heavy duty" type carafes, that may be a little harder......to throw it in the top rack.....