Multimeter Nonsense Readings

[phillium]

I recently bought a lot of multimeters with the description "Some Work, Some Don't" and now I'm trying to figure out what actually needs fixing. Some of them seem to measure correctly, but will display either offset (ie nonzero) DCV readings or constantly climbing readings when not connected to anything to read. Is this actually a problem, or is it OK as long as they read a known value correctly?

PS. All of the examples I can remember do this for DCV specifically, not ACV or impedance or anything else.

[Greybeard]

High impedance adc tend to count up or count down display due creeping currents.
If shorted input is steady near zero it's OK.

[bdunham7]

I recently bought a lot of multimeters

Before you ask us to think about multimeters, please tell us exactly which models you have so that appropriate answers can be given. 

Meters with high-impedance ranges do drift up or down on the lower voltage ranges when there is no input.

[phillium]

The two I'm most concerned with are Fluke 8808A's, although I still have to take a harder look at a couple of Keithley 2700's.

Edit: After shorting the inputs I saw stable, near zero DCV readings. Thanks for the tip Greybeard!

[bdunham7]

The two I'm most concerned with are Fluke 8808A's,

Those are high-impedance in the 200mVDC and 2VDC ranges only.  In those ranges they will slowly count up or down as the small input bias current charges up the input capacitance.  20V and up ranges are 10M and won't do that.  As you've observed, shorting the inputs brings the input voltage back to zero.  This behavior will not affect actual voltage readigs because the input bias currents are very low, tens of pA.