So we have been moving house and last night I dropped a box that contained, among other things, my UPS.
Can anyone tell me what safety checks would be good to do before putting it back to use?
You could open the unit, (with the battery and power removed) and check that there is no signs of damaged circuit boards, ie cracks in tracks or fibreglass especially where heavy components are ie transformers, large chokes and electro caps, check that battery as tech14 says also check the cables and terminals.
Is there any external sign of damage to the case (ie cracked corners etc)
Plug it in at someone else's house.