It's perfectly normal for a multimeter to not read zero V when the input is not connected/floating. They have a high input impedance and will pick up noise and static electric charge.
Your bench may be noisy - ungrounded or non-conductive/ESD mat missing, noisy LED lighting, static charge on your body etc.
Nearby cellphone/WiFi packets will also cause readings to jump around.
Why are you blaming the multimeter, it's calibration etc.?
Short the input and see if you read a true zero. If you don't then there is a problem.
The supercaps are known to take the piss and leak on the board as well.