Asside from Gordon's visual checkout of the physical condition of the instrument, you can do an operational check out by connecting the theremin to an amp, and set up in the middle of a room. Turn on the theremin, and set the pitch knob to the 12:00 position, wait 15 to 20 minutes for a warmup period, and see if you can get zero beat at the proper location, ( near the volume antenna ).
There is a possibility that internal adjustments may need to be made as a result of the instrument going from one climate, to another as it travels to you. But hold off on testing, and adjustments for a few hours while the instrument acclimates to it's new environment, and then do the check-out.
make sure the instrument has had a 20 minute warm up after switching on, before doing a full check-out, or adjustment.
Make sure your amp's volume is about one third up, and that the sound of the theremin is strong enough for comfortable listening volumes.
You can tolerate reaching zero beat with the pitch knob adjusted to either the 10:00, or 2:00 positions.
Also, check the volume antenna response. Set the volume knob full right, and see how the instrument responds. You should get a nice, snappy response. Then, try setting the knob to about the 12:00 position, and see if you get more of a gradual response.
The next thing you want to check is the tonal charactor controls. Try adjusting the wave-form, and brightness knobs. If you get a bright flute like sound with both knobs to full right, and a more subdued brass-like tone with knobs facing each other, and a bright, brrassy, tone with both knobs full left, then the tonal controls are good.
Also, one last thing to check out, is linearity. Etherwave Standards have two zones of non-linearity. The first octave nearest zero beat (not generally played much), and the last two octaves nearest the antenna have notes which are closer together than in the rest of the field.
The majority of the field should be relatively evenly spaced within about 3 or 4 octaves.
Also, if your theremin does not do hickups as has been reported in an older thread, then you should be good to go.
If you find that internal adjustments are needed, consult the owner's manual (available at moogmusic.com for free download).
That's it for the operational check-out.
All the best.