Is this a linear pot or rotated pot? Have you tried replacing it with another? It may be the pot or it may be something else - difficult to tell from the given info.
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Hello @pixip
To provide a helpful answer the very minimum we need is code and a schematic of how you wired it it up. Also helpful are links to the actual products you have and photos of of what you have made.
You are streaming data very fast and, perhaps, flooding the serial port. Try this code that slows it down to 10 samples per second. And gets rid of the use of the potentially problematic String class. Does this improve things?
If you want to add some stability to the readings from the pot, put a 0.1uF cap from the wiper to ground. That will act as a low pass filter to bypass higher frequency noise to ground.