Nothing makes an engineer more nervous than a "tape-out" - that moment you send files off to a manufacturing house for PCBs (or chips). Will the returned product be correct, letting you continue on to manufacture? Or will there be a (dumb) mistake, setting you back 3 weeks and hundreds to thousands of dollars? Even the best engineers I know still get antsy and nervous in the lead up to a release!
That's why it's so important to do everything you can to avoid problems. Now, there's not one engineer out there who has done nothing but fab perfect designs each time. Heck, even Microsoft had XBox manufacturing problems, they happen! But every step you take to avoid an easily-fixable problem is worth your attention.
Before we send of PCBs, of course we do a ERC/DFM check inside the software but even then, we always take a look at the final GERBER files before they are zipped up and sent off to the fab house.
GERBER is the file format for PCB contents, it's pretty much the universal format, it's based on old photoplotters and is a readable text file which is kinda awesome because there's few parsing problems. It's not terribly 'human' readable so we suggest using a gerber viewer. Look at each layer, especially in combination to make sure everything lines up and looks right!
For example, here is a panel of ADXL345 accelerometers we had sent out. We used pink for the top copper, green for the top mask and white for the top overlay. Sometimes seeing the layers in different colors or combinations lets us see something that is amiss!
Since we do most of our development in Windows, we use GCpreview - an excellent freeware/trial viewer.
In the years since we wrote this, GC preview is no longer free. Instead, we recommend ZofzPCB which is 3D and amazing! You can also try online Gerber viewers like https://gerber.ucamco.com/
If you're using open source systems, gerbv is excellent as well.
If you're in a rush and just want to look at one layer, you can use the online CircuitPeople SaaS- we found that it didn't work that great with more than one file or large files but it does work.