I look for (in no particular order):
Someone who has a natural rapport with children.
someone who I think will be happy to go along with my wishes and not take offence if I ask them to do something differently.
Someone who I think will use their initiative.
Someone who doesn't mention the naughty step when I ask them about discipline (or at least mentions other methods of encouraging good behaviour before mentioning the naughty step).
Someone who talks about activities other than messy play.
Someone who is active and fit and likes to walk places.
Someone who I think I will get on with.
Someone for whom being a nanny seems like more than just a job.
Someone who hasn't taken many days off sick in the past.
Someone who is happy to keep to our structure of activity in the morning and sleep at home (or at a nanny friends house every now and then) after lunch for my youngest.
Probably loads more but mostly it's a gut feeling.