Is my iPhone 4 touchscreen malfunctioning?

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:

iTunes: Backing up, updating, and restoring your iPhone, iPad, or iPod touch software

There are a handful of utilities that you can use to test responsiveness of your iPhone.

Try using a webapp called Sparky in order to test and see if there are in fact dead spots, alignment issues, or any other problem with your iPhone's touch screen.