things that come to mind and I have experienced:
-put on turntable and check if the hole is centered (check this also for the final batch)..have a close look at the cartridge while the record is spinning..if the tonearm wiggles from side to side the centering was bad...
-check if the TP is flat and not bent...(check this also for the final batch)
-mono check the testpressing ( I once had a bad laquer cut with severe phase issues cut from 1/4"tape..turned out that the playback machine was not alligned properly) it sounded ok in regular stereo, but when mono´ed everything above approx 8k disappeared
-playback the TP on a low grade turntable and check
if it jumps the grooves...sometimes narrow cut records will play very well on technics 1210 etc. but skip heavily on cheaper players, because there is not enough "land" between the grooves...also phase issues in the low frequency range can result in shallow grooves that make the cartridge skip..
-check for clicks and pops..I had a TP where the laquer was not treated properly by the pressing plant, so every copy had a small (almost unvisible) scratch, which coulds be heard as a click on every copy...
- lately I only do attended sessions when it comes to cutting the laquer..(first of all because it is much fun)
Once I used a plant that offered pressing including the cutting and on the
testpressing one track turned out to be reduced about 3dB compared to the other tracks...I complained and they recut the thing with sounding good..there was no
apparent reason why they lowered the volume on this track (it did not have excessive bass or highs when compared to the other tracks..that would have risked a bad transfer or risked the cutting stylus!!??)
So check, if the person operating the lathe changed volume or eq on some tracks and if this is acceptable to you
- check if the visual markers are set properly..
once had a copy where the lathe operator set a marker during a break/dropout/quiet passage during the track