Well, the PT140 is not know for its accuracy, and has a really poor trigger for target shooting. It was designed as a low cost, safe (long and stiff DAO trigger), small and light, high capacity, close range self defense handgun, primarily for concealed carry.

It excels at what it was designed for. It sucks as a target pistol.

Let others shoot it, and try shooting it from a rest, to see if the sights are off. Because of the long trigger pull, I've seen some shooters dip the barrel before the trigger brakes. I personally think these guns require some extra concentration and practice to get accurate hits because of the long trigger pull.

Start off with the target about 3 to 5 yards and work your way back. With a new firearm it is much easier to find the bullets point of impact compared to your point of aim from close up.
Good luck.

The Heinie sights use a "Dead on Hold" not the "6 O'clock Hold". On the Heinie, the front dot should be directly on the P.O.I. If you use the standard 6 O"clock hold, you'll always shoot low.
Over at TaurusArmed.net this has been a common topic.
This system is meant for quick aquisition, defensive shooting, not bullseye shooting.
The following article was written by the sight maker, not Taurus. http://www.heinie.com/taurus.php

I used my PT 140 in my first ever bulllseye match. It was dismal at best. The long DAO trigger is horrible for any kind of aimed shot. The shortness of the barrel is just as bad. Out of 60 shots, only 6 hit the target @ 50 and 25 yds. As stated above, this is not a target pistol by any stretch of the imagination. It is best suited to the job it was designed to do, self defense. Step a little closer to the target, about 5 to 7 yds. You will find it more than adequite at that range.

Posted from my iPhone.

If you're new to handguns it's fairly likely you'll need some practice (training?) to avoid some of the basic technical mistakes - one is to push into the trigger stroke (anticipating recoil) this will put your point of impact low. The comments from the other fellows also apply - the sights are a little different from other guns. And finally, as already mentioned - the purpose of the pistol isn't for long range target shooting - it's a defensive handgun, and targets beyond about 7 yards is asking too much (and in a defensive shooting could beg difficult legal questions).