I have just brewed for the first time. After bottling,I noticed the air lock, which I hadn't removed, was missing its water. I'm assuming the week-old air lock water was sucked back into the brew as I was filling bottles from the bottom. Could this contaminate the brew? Should I throw it all away and start again?
If that is indeed what happened, it might introduce some bacteria that could give you off-flavors, but it won't make it unsafe to drink. I'd at least wait and see how it turns out. If you try a few bottles a few weeks down the line and they end up being nasty you could consider tossing it, or turn it into vinegar or something. But beer is a hostile environment for a lot of bugs and you might end up with something perfectly drinkable.
Of course this is exactly the kind of contamination you strive to avoid as it can make your beer taste quite a bit less than ideal, but this batch may not fare too poorly, especially if you drink it sooner rather than later.