Problems with giving water - can cause diarrhoea (somewhat counter-productive), and can fill their teeny bellys (meaning they don't take as much milk, and so lose out on valuable nutrition).
As long as you stick to little and often, you'll be fine.
I suggested on a thread somewhere yesterday... Use a medicinal syringe (comes with calpol), well cleaned, and squirt water into their cheek (not straight into their mouth so it goes straight down their throat and makes them splutter).
A - You can regulate tiny amounts, so you know they're drinking it, but not gulping loads.
B - minimal mess.
C - Handy for those BFing mummies that wish to give a little water also, but don't yet want to introduce a bottle.
As above, just make sure it's freshly boiled (not water that's already been boiled earlier), and left to cool.
Store this in a bottle or wherever, and syringe some out through the day.
Maybe give a short while after feeding, so you know they've had their fill of milk first xx