Ugh, my family and I just went through Au Pair hell. I don't think that our situation is that typical, so feel free not to read on. We needed someone to care for our 2.5 year old DS1 initially, and then to watch DS2 once he was 12 weeks old (he was born in July).
Our first Au Pair started at the end of May. She was very gung-ho about working for us, very enthusiastic. However, she put all of her efforts into cleaning our home, rather than caring for our child. She never did any craft-type activities with him, despite being asked to, given supplies for, etc. The worst part was that she had many lapses in judgment that led us to feel that DS1 was not safe with her. Also, she was out partying at 4 am 3 days after DS2 was born and *lost* our car. We had to report it stolen, it was a huge pain at a bad time, and this was just typical for her behavior. The car did eventually turn up as having been towed (she parked illegally). She also broke 2 cell phones that we provided to her, set 2 items in the kitchen on fire on 2 separate occassions, let our son play with a sewing machine and a pincushion filled with pins (these items were out of his reach but she left him unsupervised for long enough for him to climb up on top of a table and get them. He actually had enough time to pull all of the pins out of the cushion and scatter them on the floor). She also left DS1 unsupervised in the house for 10 minutes - my husband saw this one morning when he left for work, then realized he had forgotten to do something in the backyard. He watched her leave the house, go to her apartment (which is detached) and stay up there for several minutes with DS1 alone in the house. Not OK with us.
So, the agency agreed with us that she was not a good au pair for us (the scary part is that they rematched her with another family!). We rematched with a second AP who seemed much more mature, even though she was only 21 (the first AP was 24). She was also a better driver (she was German, and I think that in general their standards are much higher) despite only having a driver's license for 6 months prior to her arrival. BUT, she became very homesick and left us after only 3 weeks, giving us only 3 days' notice. She claimed that her mother became ill, but I'm not sure that I completely buy her story...she seemed very guilty in all of her apologies, etc. Also, she had a serious boyfriend in Germany and I think that was a factor in her decision.
So, 2 au pairs in 3 months. This cost us a lot of money, and it was a huge hassle to have new people in our home to train, get to know, etc. The worst part was that this was a lot of transitions for my sweet DS1 to have to deal with. He skipped naps for a week every time a new AP started. I don't think that we will ever do it again after this experience.
Once the agencies have your $, you are really at their mercy. It is up to them whether you can rematch if it doesn't work out, etc. Our case was actually so bad that the agency is surprisingly giving us a partial refund. This is very rare.
We just hired an experienced nanny (you can see one of my earlier posts about this) and it makes a world of difference. She is excellent with DS1, he is laying down and taking naps for her without any problem - even without someone staying in the room with him (!!), she is very gentle, etc.
Yes, a nanny is more expensive. But, it is also much less hassle than an AP and if you can find a good one, they are much much better IMHO. YMMV. Good luck!
Feel free to pm me if you have any more questions. Sounds like others might be better at picking out au pairs than I am...