If they were very inconvenienced or very upset, you could refund 1 or 2 nights, or a percentage across the whole booking. I have done this in cases where my boiler wasn't working, and there was no heating or hot water in the flat.
If they weren't very inconvenienced, you could give them a bottle of wine or a voucher for a local shop.
If you have accidently damaged some of their belongings, I would offer a payment in cash.
Don't forget that if you offer a partial refund through Airbnb, the guest will not get that money until the next time you get a payout from Airbnb (the refund will be deducted from the payout). This is ok if you have lots of bookings lined up, but not helpful to the guest if you have no bookings in the next few months
Compensation varies according to several factors; i.e few days back a good host [from Turkey] came claiming the Guest Killed his Cat! [guest's actions - leaving window open - having been told several times DONT do it - led to the cat escaping & dying in the streets] And while we have no reason to disbelieve him [he told AIBRN, Cops etc] it goes to show that compensation/ damage 'is a wide concept' ... in the end it has to be calculated in case by case basis & as you say 'when things go wrong'