The positive spin... She's fostering independent play!
I don't know if she's a good nanny or a bad one, but I don't pay attention to my kids every second of the day either. Play dates and even computer use are not bad things.
I used to be a nanny and I had a lot of time that wasn't actively involved with taking care of the child. Children like to play alone and should be allowed to if they are having fun. They also take naps. I did playgroups so that I would have a break and also so the kids would learn to play with others. I would always go with your gut feeling if you feel like your baby isn't being properly cared for, but playing on a website and letting the kid entertain herself a bit doesn't equal an inferior nanny nor does it mean a nanny cam is needed as someone else mentioned. A lot depends on what website was left up. Also, you can check the history on the web browser to get an idea of how many sites she was cruising on.
But it is hard when you had one you liked and then get one who is less good. If you aren't feeling the vibes from this nanny, change nannies. It is important for the family to trust and get on with the childcare provider.
Put a password on the computer. I would not be as concerned with a little computer use, but I am not sure if I want somebody else on my computer. Especially since I have work stuff on mine.
The new class I'm in at Gymboree is full of nannies. The range is really shocking.
One nanny actually held her charge by the shirt so she didn't have to chase after him.
Then you have others that it's obvious love the kids and vice versa--like one who is really involved and seems to really get a kick out of her charge's personality.
It has opened my eyes a lot in thinking about what I would want with a nanny for J. And I think if you aren't sure/happy, fine, discuss it, but ultimately, you need to feel confident that all is well.