My iPhone4 is weird. The bottom touchscreen can be slid (to unlock) but it's really hard to tap the app in the bottom area. It seem the bottom screen is not sensitive but I can slide to unlock. What's wrong with my iPhone?
It is almost certain that you have a hardware problem, something wrong with the actual touchscreen. Since the iPhone 4 is less than a year old it's still under warranty, Apple will fix it for free.
If you haven't done so already you can try a complete restore of your iPhone, erasing everything and returning it to it's brand new state (after backing it up). Odds are not good that this will fix it, but it's worth a shot, especially if having Apple repair it is a hassle.
Apple explains how to back it up and restore it here: