What should I check with set up of a tandem?
In addition to the pre-ride checks covered here, I suggest you check that:-


The sync (timing) chain between the front and back pedals is not too slack. You can expect it to move a centimetre or two closer when pinched, but visible droop is bad news and might be causing feelings of sudden changes of cadence.
The pedals are in phase. That is, the right pedal on the front is at the top when the right pedal on the rear is also at the top. Some tandem teams prefer to be out of phase, but in phase is standard and easiest for a beginner. I would expect all hired tandems to be in-phase.
The tires are suitable. As tandem tires carry more weight, it is worth having wider, tougher tires. On a road tandem I would say 28mm is a minimum. My wife and I use Schwalbe Marathon Plus 35mm (1.35") and we aren't heavy.
The tires are at high enough pressure. As above, the right pressure depends on tire width and rider weight, so is generally higher for a tandem.
There is no keel tube/chainring damage. The bottom horizontal tube between the two bottom brackets can sometimes hit the ground if ridden over bumpy surfaces due to the long wheelbase of a tandem.