I havent had much experience with a 405,ive heard they are good machines. A few things id look at.
Does it start up and run ok?
How does it travel. Are the tracks worn, adjusters on tumbler shaft stretched out
Does it switch from swing to travel easily [ I doubt it has independant swing and travel]. See how it steers,watch the tracks dont peel off if they are worn.
Have someone swing it back and forth tell them to be a bit rough and watch for play in the turntable rollers and in the boom foot pins.
Look at the brake linings and frictions on the drums and linings on the swingers.Are they worn thin at one end of the band or shoe ,they should be a consistant thickness all around
If you can see or feel a bare spot on the drum surfaces feel for ridges ,they should be flat or smooth.
Does it look like it has been well greased and kept up.
Check the cable, boom hoist in particular look for crushing or broken strands.
Run it your self see how the swing feels can you swing one way and stop it smoothly . Does there feel like a lot of slack between swing directions, any clunking or grinding while swinging.
Have the owner lower the boom,find out if it is live or power down. Look at the boom tip sheaves,are they worn sharp on the edges and rattling around,if so its had lots of use. Look all of boom hoist cable over again while its down all the other cable is important to,but that one causes disaster when it fails.
See if theres a drain cock on the bottom of the house,near the turntable when the machine is swung forward on the tracks,check it for water it should have oil in it.
Theres a few things to look at,im sure others will add to my list. One thing to remember is these old machines will be worn and still do lots of work. If everthing functions its probably ok.