I didn't read every word of every post so I hope this isn't repeating, but is it possible that she's from a culture or just a family where it might be considered "part of the payment" for an employee to treat certain household items as if they can be taken to her home? I note that the things that are missing are very, very mundane -- a Swiffer, measuring spoons, plasticware. Not jewelry or anything else, right? I am NOT saying let this go because it could escalate IF she is just a thief, but I wonder if she is from someplace, or from a family, where employees might consider these cleaning and cooking items to be something it's fine for them to take home and bring back whenever they like....? In her mind is she just borrowing these mundane things? They aren't things she could sell off for cash. Again -- she should not be doing this at all but it might be a cultural disconnect rather than pure theft.
I think you do need to deal with this. I would sit her down (when the child is napping or otherwise occupied) and tell her that you wanted to ask if she was "borrowing" items like the spoons, plasticware and Swiffer. She needs to know that even though these are very cheap everyday items, in your household they need to stay put.
But I'd still start hunting for another nanny while you still have her around to cover you. The reason is much bigger than these petty thefts:
I would be highly concerned about the fact you and she can't communicate adequately, frankly. What if your child were sick during the day and the nanny couldn't adequately describe the symptoms to you when you got home? Does she read English adequately enough to give your child a dose of medicine if needed? Would she be comfortable calling the pediatrician for advice or taking your child to the emergency room by herself? If she takes your child outside the house to any play groups or the park, I would be uncomfortable with her doing so because how would she communicate with others if your child ran off or got hurt? I would let her go just on that basis. Your child WILL get over the transition; young children adore anyone who is their caregiver, frankly, and it's up to the parents to ensure they get a caregiver who is the best one for that child -- even if it means letting go of a caregiver the child seems to love. The caregiver and the parents need to be able to communicate AND the caregiver has to be able to cope verbally when she is in charge of the child and an emergency happens without the parents available to handle things.
ADDED: I see someone decided it's "obnoxious" to mention that maybe the nanny's English isn't adequate. Well, the original poster wasn't clear that the nanny's English was OK; she only added later that it is. I do know people who hired nannies who were great with the kids but whom the parents said they were concerned about if there was an emergency and the nanny had to call an ambulance or take the child to the ER. I'm glad it's not the case here. But there's no need for other posters to name-call just because some of us dared bring up the idea that a nanny might need to communicate well in an emergency.