Is there any chance its just the high input impedance? The DC offset issue you're describing sounds to me like it could be explained by high input sensitivity.
Please excuse me if you already eliminated this possibility but - on the off chance you havent- some people might not realize that these voltages are always there..
If you do simple experiments with high gain op amps and FETs (with very high input impedances) you realize quickly that there are varying voltages on everything all the time, and they change a lot. Anything that is (well) insulated from the ground will collect charges. Especially when the humidity is very low!
You know, the ESD we are familiar with -
But regardless, ekretz, even if your scope is not simply remarkably sensitive and is measuring ESD for you, please step back and take a breath and look at the comparable products out there at that price, and the discussions about them in other threads, to get a broader perspective on the situation before jumping to negative conclusions.
certainly some vendors sell crap products, but this one does not seem to qualify as one under any definition of that term. Instead they made a remarkably high quality product available at a very low price.
My old Tek 2211 scope has a very high sensitivity input setting (its one of only a very few Tek models that do) and when its set to that range, sometimes it also picks up DC in the air, when its very dry. It has nothing wrong with it.
Although the humidity today seems much higher than it was a few days ago (when I was testing a power supply I was fixing.) when I last observed this. I can usually tell when there is a lot of static electricity in the air from the amount of little sparks I hear when I touch things, put on a woolen sweater, etc.
You can also set up a simple circuit to measure it using a single FET. If you go to Techlib.com there is a wealth of circuits for things like a "Ghost Detector" which act as sensitive electrostatic field detectors.
A few years down the line, you might in retrospect wish you had eliminated that possibility before you returned what may be an above-average acquisition.
Please disregard my comment if you have already eliminated this possibility.
But since non-deterministic behavior in electronics is unusual, I think its not unlikely that its measuring something real, and it seems likely that ESD is it.