It's a thing of beauty Caleb though I know there are those who will disagree.
With a bandwidth of 400 Kilocycles / sec (they hadn't even started using Hertz then!) max 2.5 MC/s there's not a lot you could use it for now. If it works you could make a clock of it - didn't you post an article on this recently? Or have it on the corner of your bench displaying Lissajous figures.....
From the looks of it there is no reason it should not work, though you may get the standard problems with dry electrolytics, but they are easily replaced.
I am also circa late 50's and used this scope when I was a kid. For the younger crowd, an interesting aspect is the long neck of the CRT which is because scopes used electrostatic deflection rather than electromagnetic deflection. Faster, but a narrower deflection angle.
@Caleb: The surprising thing to me was when you took the cover off -- seeing how few components were used -- I was expecting it to be jam-packed with circuit boards and transistors -- I hadn;t realized it was vacuum-tube-based.
As a rebuilder of old tubed Heathkit ham gear, you NEVER just turn on the power and see what happens.
The 60 yr old paper caps on these pieces are almost 100% quaranteed bad, open or shorted. And those bad caps can damage irreplaceable components on failure, like hard to find transformers. And a surprising number of carbon resistors crack with age.
Step 0: get and read the manuals
step 1: replace the paper caps with modern high quality (non-Chinese) electrolytics
step 2: clean all the switches, pots, sockets
step 3: test the tubes
step 4: use a variac to SLOWLY bring up the line voltage to avoid in-rush issues with components which have not seen a magnetic or electric field for half a century.
step 5: if it works, rejoice, if not troubleshoot and find the dead guy(s).
step 6: Enjoy the rebirth of someone's old friend.
@R Sweeney - Excellent advice, and when I said it probably still works I should have added the caveat about the electrolytics. Written in haste.....
Very few people have a variac or a tube tester to hand. A test of the disconnected electrolytics with a lab PSU at maybe 50V is a good start. If you're in the US you could then use an isolation transformer (a must) and a rectifier with a beefy 10K resistor in series to put about 160V on them, Leave it on for a bit , monitoring the current (should go quickly to a few mA or less), to let them reform. But caps of that age will usually be dry (= low cap) if nothing else.
If you can just replace the electrolytics (which is probably the best way to go) then you'd probably be fairly safe in trying a switch on, with a meter across the main electrolytics - if the voltage does not go up to a few hundred volts right away then switch off and dig further.