From my experience, department store bikes are lower quality, but the main problem is who built the bike. It was not built by someone who was trained in bike building, it was most likely built by the guy who gets paid minimum wage to work in the sports dept. Because they are lower quality, they are hard to adjust and build anyway...add to that the fact that an untrained person built it and you have an unstable bike.
My first thought would be to check over the bike completely, and if you don't know how to, get a friend who does. Make sure the wheels are true and are installed correctly, make sure the bottom bracket and the headset are installed correctly, and make sure everything else is straight...including the frame. The frame and fork are hard to check without the proper tools, and I doubt the dept. store checked the frame and fork for damage when the received the bike.