You cannot get a 'false positive' - i.e. if it says you're pregnant, you are.
You can get 'false negatives', where it says you're not pregnant but you are.
The reason for this is that when you are pregnant, your body quickly starts to produce new hormones and it is one of these that pregnancy kits are set to test for. If the line is faint, it means there is not yet enough of the hormone to produce a stronger line, but it will happen if you wait for a few more days.
However, it is possible to test pregnant and then test not pregnant some days later. In this case, it does not mean the test was wrong but that the ball of cells had not managed to successfully implant in your womb - i.e. you were pregnant but now you're not. It is highly unlikely you would notice when the remains of that failed pregnancy passed from your body.