You should just forget about the batch. It's ruined. Send it my way.
Kidding, of course. There's no harm in tap water falling in the beer. I've had MUCH worse fall in a beer and it turned out fine. What I've learned in the last 4-5 years that I've been brewing is...it's a lot harder to screw up a beer than you think. I've infected one beer in that time, and that was because I used a bottling bucket to ferment in. The bottling bucket had grime left over in the spigot that I didn't notice and it infected the batch.
There's so many horror stories out there that it's hard to imagine why people get into this hobby in the first place. Most of those stories are scarce though. They say that most people infect a batch of beer around batch 10-15. Why? Because you're still learning what can and can't be done. If you haven't infected one by then, chances are you'll know what you're doing enough to not have any problems.
To answer your question, 2-3 weeks is about when you'll start to see mold or a pelicle form. But, if you do gravity readings every week or so, you'll notice when the gravity starts dropping a lot farther than it should.