I purchased a 2002 C240 a few months ago. I bought the car from an individual, the car was in great shape it only had 75k miles on it. I purchased the car with the check engine light on, which has turned out to be a challenge. I took my code reader with me and saw that the CEL was Cylinder 4 misfire, I thougtht no big deal. When I drove the car home it seemed somewhat underpowered, so I changed all the spark plugs and the checked all the wires, which were all ok and that seemed to fix the problem. Around a month later the CEL popped back on and it was again Cylinder 4 misfire. I went ahead adn changed the coil and both plugs and plug wires for that cylinder to take car of the problem and not take any chances. Again all was good for around a couple weeks. Then the same has happened again. CEL on and Cylinder 4 misfire is the code, but this time in the display it said battery/alternator visit workshop, could this be tied in together? What else could be the issue for this one particular cylinder, am I thinking right that if it was a CAT converter problem it would throw the misfires for every cylinder on which ever side was bad? It runs really bad when the light comes on, I thought about the MAF, but I thought it threw a particular code not a cylinder misfire code. Any ideas? The last time I changed the plugs on cylinder 4 they had a lot of gas on them, making me think it may be a bad injector.

Yes, more likely a injector issue.

Could even be related to crankshaft position sensor out of phase.
Aligning the flywheel sensor rotor adaption would be a good starting point.

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Could change the injector or coil to a different cylinder to see if the failure then moves to the new cylinder,

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The alt/battery is not related. However that likely means you've lost the regulator, fairly common for that generation. It could be the alternator itself, but I'd shoot for a regulator first, unless you also have bearing noise.

On the misfire, I'd vote on an injector as well. If you don't want to dump more money, swap it with 5 and see if the misfire follows it. If not, then it may be the injector connector, there are repair kits readily available for that so apparently they're not 100%. That said, I'd think a failing connector would cause fuel starvation in a cylinder, not overfueling. Still, I'd swap the injector with the next cylinder and see what you get.

Replaced the injector, everything is so far so good and it seems that Im getting improved fuel mileage now.

I'm not saying that this is the reason your Mercedes is misfiring I'm simply offering my opinion based on experience. The ecu controls the injector pulse, cylinders and all the sensors. So if your Benz misfiring make sure you rule out the ecu 1st. If the ecu is the culprit then here is some good information on how to test it and remove it. How to remove a Mercedes C240 ECU control unit

Good luck with it