I always think of an AP role made up of 3 areas: childcare, cleaning, cooking. I don't ever expect any APs to be good at all three, so for me the childcare aspect is the most important, and the other areas I'm prepared to be less fussy on. On the trial weekend I focus on the childcare aspect. I don't set up any specific tests as such. Our APs spend a weekend with us and we take them on a day trip to London. I observe how she is with the kids generally, how she interacts with them, how she is with them on the roads etc. I don't expect her to do any household jobs during the weekend, but if she offers to help, I consider it a huge plus and shows she has a bit of initiative and willingness. In my opinion, i think you can tell if someone has a natural rapport with children within a few hours. I make it quite clear that the weekend is an opportunity for us BOTH to get to know each other better.
Also, I think at a trial weekend is a good indicator of their attitude generally. I have had one that literally wanted to be waited on hand and foot, barely spoke to the children, hid in her room at every opportunity and woke up on the Sunday morning at 11am!! Needless to say we didn't take her on, but interestingly enough she decided later on that she didn't want to be an AP anymore.
It is far easier to decide if the AP is a no-go after a weekend rather than go through the inconvenience of having her arrive and decide after a few weeks she is not working out.
Blueshoes - I've had a couple of APs who were brilliant at folding clothes but actually quite useless with the children. My latest one however was very lackadaisical over the very little housework she had to do, and yes - I do agree with you, she was generally disorganised, needed constant reminding, and generally didn't care about doing a good job. I got rid of her in the end. An AP role is generally quite simple, so anyone who still needs constant performance managing after a month is never going to improve.