First, all parents want their child to have “a really fun time,” but they also don’t want to come back to find their house (rental or not) looks like its been ransacked by a band a marauding pre-schoolers. Cajole the kids into helping you pack up the 20 puzzles you've done together, put the dishes in the dishwasher, put the markers away, legos in the lego box. Parents are not expecting you clean up after them – only that you leave the house habitable and its not that hard. In the distant future, you will find yourself doing these things on a regular basis.
Second, if the mother mentions that her 3 year-old seems “a bit crabby today,” nod politely and hope he hasn’t tuned into evil-child incarnate. Don’t chime in with commentary about how he screamed for 2 hours and tried to head-butt his baby sister the last time you were there. Chances are, she’s merely trying to acknowledge that her child is not uniformly delightful; she is not inviting critiques.
Finally, if the parents seem a bit tipsy when they come home, they are. Just take your payment and get out of there. Don’t let them embarrass themselves. They’re like 40 or something, after all. And you will be too, before you know it.