It's like any person we hire to work for us, whether it's a plumber, electrician or builder etc we are hoping that they are good at their job and that their references are real and not made by friends and that they'll do the work we want them to do. The only difference here, is, that this is your child so of course you want to get it absolutely right.
It can take time to find a person that fits with your family. Not everyone is going to be perfect and it's trial and error. The positive you can take from this, is that you are now more aware of what you need and expect.
I would probably lay out at interview stage what you would require from them. Basic things that we would assume they would do like washing child's food utensils, sometimes it has to be spelt out, however I do think making a list of what you expect is not unreasonable, you don't have to sit there rhyming off your list, you could have it discreetly in a note pad and just refer to it when you need. Or make a joke saying that you've made a list, you promise you're not weird but it helps you to remember everything that's important to you.
During the interview you can discuss what play, learning etc that you like, or ask them what kind of activities they suggest.
It breaks my heart when I see the nannies beside me basically ignoring the child, my ndn use to run a creche for her friends, the greetings in the morning were so over the top, I could hear the HELLO, HOW ARE YOU, GREAT TO SEE YOU, YOU'RE FAB, YOU'RE THIS AND THAT, and then as soon as the car pulled away the pram was shoved out into the back garden for the day, rain covers in winter, blankets over prams in summer and she sat sunbathing or on wet days I'd hear her hoover going for hours.
Children adapt easily, don't worry about changing nannies, when they start school they will have regular changes of teachers. There's no harm in them getting use to different people, it will stand to you when you want to have a night out or a weekend away and use different people /family to babysit.