Run a TEST command from the front panel and note if any errors are reported. If any errors are reported these can be decoded with the ERR? and ERRSTR? commands.
When the DVM has warmed up sufficiently run an ACAL ALL command so the that meter runs through a complete self-calibration and check any errors reported. Note: the ACAL ALL command takes about 11mins to run.
These DVMs use a battery-backed RAM chip to store critical calibration constants. If the battery runs low then the unit needs an expensive trip to a cal lab for full recalibration. Loss of battery power will usually be indicated by a RAM checksum error message during power-up.
If the units are more than 10 years old a battery replacement is advisable. Earlier units used a Dallas chip with internal battery, which is long out of production and unobtainium. Most users opt to replace this chip with alternative NVRAM chips; there is plenty of info on this forum about substituting for the Dallas chip. Later units used an ST chip with a easily replaceable snap-on battery hat.
Other useful information is contained in the non-volatile memory and can be accessed using front panel commands:
CALNUM? records the number of calibration cycles the unit has been through
CALSTR? is a stored text string that may contain useful info regarding when the unit was last calibrated, by whom and under what conditions.
REV? will report the S/W version number
OPT? will report any installed options
You can check the serial numbers against the HPAK website:
https://support.keysight.com/s/service-and-warranty-statusIf the units were serviced/calibrated by HPAK there may be useful info on this site, particularly regarding whether the A3 PCB has been replaced to fix the dreaded U180 drift problem. To check for this drift problem you need to run the procedure listed in 3458A service note SN18A. Unfortunately this needs about a week of continuous running to get usable results and if you discover the unit is drifty the only option is to return to HPAK for service as the replacement A3 PCBs are no longer sold by HPAK.
There is plenty of other info available on the web about maintenance work required on older 3458As e.g. replacement of RIFA caps and Schaffner mains filters, general recapping, replacement fans etc.