Should I test the water in my house for contamination?
Water testing (from what I've seen) is cheap and easy enough that it's worthwhile to do if you are worried at all.  If you're in the US, check with your local Department of Natural Resources to find out where to get a sample kit.  Where I live, it's $10 for a container and testing from my State Health Lab.  

Typically, you'll need to sterilize a faucet before you take a sample (either using a torch or flushing it with bleach) and you'll need to drop it off for testing fairly quickly (24-48 hours).  This is third-hand from my home inspector (and I'm sure different labs have their own requirements for prepping and collecting the sample) so definitely read the directions you get with your kit.  I recently purchased an older home with a well and I'll be doing a test myself this week so I'll be able to follow up with actual experience soon :)