Missed it by That Much...
For example, if you look at these PCB images, you'll undoubtedly spot the problem right away. These passed the Eagle DRC. I'm not saying all CAD packages will miss this kind of thing, but you should always expect that something might get through.
Of course, if you end up selecting the wrong component footprint, or if the footprint library part was created incorrectly, the DRC definitely won't catch it. A DRC also won't likely help if you output your Gerbers incorrectly, i.e., positive output vs. negative output.
Just like you don't completely trust an autorouter, you shouldn't completely trust your CAD packages ERC and DRCs. Spend a little time manually double checking things too.
Bring out the cone of silence