Your problem seems very frustrating I am sure, keep in mind that the belt driven accessories go on and off. For instance when you first start your car the alternator really kicks in to replenish the battery, and the AC compressor cycles in and out for various reasons as well. That is the first thing I would check. Is your Engine light on? The fact that it is getting progressively worse, you hear the belt slip, and the lights go dim and bright lead me to believe that the alternator is failing. Pull the belt off (The fan shroud comes apart and out in a neat way to allow access) and see if there is any play in the pulley or if it is rough when you turn it by hand. It should turn smoothly. You may have a bearing going out. Check the other accessories as well while you have the belt off. Has the alternator ever been replaced? How often do you change your battery? I have found that a new battery every 2-3 years keeps me from replacing my alternator.
If you have no play or roughness in any accessory, I would then recommend taking it to a shop and having them hook the voltage system up to check the condition of the battery and the output of the alternator. If everything checks out ok, then take it to the dealer and have them diagnose it. I have lots of friends that have Mercedes that take them to shops, and have plenty of stories, but I find that the dealership has the best tools and knowledge for diagnosing these odd problems. Take care and good Luck!