I got a Fluke 8600A multimeter, and while its hardly a precision instrument, the basic topology is an integrating ADC similar to better meters. So I figured I can play around with it. I found that it works well and is mostly within specs except for one problem.
When first turned on, it has an offset of about 0.1-0.2 mV that takes very long, several days, to decay to zero. Once it decays to zero, the meter is stable. If I turn the meter off, the offset starts to come back after about a day.
I poked around inside with a voltmeter and experimented with shorting the input using different resistors. The offset is consistent with some leakage current going into the input stage. The board seems clean and I also cleaned it with IPA.
So my current theory, which maybe totally wrong, is that there is a hairline crack in one of the input stage FETs that makes it sensitive to humidity. Humidity is the only effect I can think of that would have a time constant of several days to "dry out". Any other ideas? I'd like to identify the problem rather than just start swapping all the parts.