. Old machines will keep you busy enough keeping them running. .
This is the advise I was given:
Necessary things to inspect, measure, indicate, etc. on the machine with a test indicator and other easily available tools
check spindle run-out with test indicator
blue toolholders to check for spindle taper wear
check repeatability of x,y,z at multiple feeds
check backlash of screws
check ways for visible wear
listen to spindle at different speeds
the "pull on a tool in spindle and see how much the machine gives" test
test cut if possible
Listen to the axes-The indicator test will tell much about their health, but I've seen ballscrew support bearings that measured OK (next to no backlash) that were noisy. Often, there is more than one bearing at each end, so one can be failing while another is taking up the backlash. However, the good one is now taking the load for both, so it's going to have accelerated wear/failure.
Try to determine if the waylube system is oiling all points properly. If not, it might be a general indicator that the machine isn't well-maintained.
Test-cut, as you say. Give it worst-case loading to deflect spindle and check rigidity.
Take an indicator, see if you can push/pull any of the axis'
Check the comp settings
Let the spindle warm up, after warm run it at different speeds to hear noise/vibration
Check the tool changer, see how well it changes tools at different areas of the tool changer
A drawbar test would be nice as well as a ballbar test on the axis'
Check the electrical cabinet for ANYTHING that looks "not factory"