What should I check with set up of a tandem? Particularly with reference to hired tandems, or when you're first setting one up.

A bit of context:
I hired a tandem today and went for a ride with my wife. I've been riding for about 20 years, she rides very occasionally (once every couple of years). She's 30cm shorter than me, so she goes on the back and I go on the front - which means it's a bit harder for her to diagnose what's going wrong with the bike as she's unfamiliar both with the components she's looking at, and knowing what 'correct' feels like).

The tandem we hired was a bit of a tank: an old hack that gets ridden up and down a path in a park a few times every week, the gear shifters didn't work (and the indicators were completely worn off the shifters), brakes didn't do much apart from suggest the bike might slow down at some point in the future, usual sort of decrepitude, but as we were only going on a very flat bit of tarmac, none of that was a big issue.

When we were pedalling, there often seemed to be changes in how much feedback and force my wife was getting/putting through the pedals - sometimes it would feel that she was pushing much too hard on the pedals, and at other times she felt that I was upping the cadence without warning - which I don't think I was. Could this be caused by the chain betwee the front and rear cranks being misadjusted - and if so, what can I do to check that before riding the bike away from the hire shop?
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.