Ok, crime on Waiheke lower than the rest of Auckland I believe. Wouldn't surprise me if it was the lowest in Ak tbh. Don't know any figures though. And the supermarket has always been quite empty when I've been in it 
Yes, Eastenders is on, I don't watch it but I think it's only a few months behind the UK (I'm a Corrie fan myself).
These figures are monthly, yes?
Rent - don't know much about rental costs anymore, 475/wk might not be that much in some areas of the Shore but I'm sure you'd get something for that.
Phone/electric/insurance costs look ok (electric may be more if you try to keep a house warm to UK standards in winter)
Petrol - that would be for you during day as I assume the bus pass is for yoru dh to get to the city? 100/month fine for daytime driving for you, would be more if your dh driving to city and back every day. We are 13km from city centre and my dh puts about $200 petrol in a month I think. I prob put about $50 a month in, for me driving in daytime with dcs.
Gas/other - lots of places don't have gas so you may not need to budget for that - you could add it to your electricity bill maybe.
Clothes - I don't spend $200 a month on clothes but I easily could if I had it! Im a bit of a second hand shop/bargain hunter though (and we get lots of kids stuff passed on to us from friends).
Playgroups - $150 a month? The one I go to is $2 per family per session (twice a week) so that would be $16 a month. Or are you meaning "activity" type things like music groups, baby gym etc.
Mobiles - I strongly recommend 2 Degrees, way cheaper than the other 2 providers, I find.
Only thing I can think of not on there is Sky - or are you not going to have that. We pay about $70 a month for it. Eastenders is on Sky here...