Does it make sense to buy a Nintendo Switch second hand? What should I look for, besides that the console is clean and the screen has no burn-ins or dead spots?

ask if it was hacked because there is a chance that it is banned from online services and the eshop.

We bought ours new just a few months ago, mostly because people sold them second hand for not much lower than new. But I'd say check the followimg:
- the kickstand, it's flimsy like hell unless you get the new oled version
- make sure the controllers snap in to place properly and aren't loose
- the joysticks tend to aquire a bit of drift and get a bit sloppy, so check those

If you’re in the UK CEX have a good returns policy and a 24 month warranty.

I quite fancy a new switch oled but I can’t quite bring myself to part with the money.
And I don’t know if they’re that that much better than a standard one (I don’t own either).

nintendo consoles don't get devalued, so I'd only look for a second hand one if i wanted it to be unlocked

also there's the drift issue

oh and there's a second version of the console that has better battery charge, you should check which version it is