Hey there,
A really good test to see if this is software or hardware is to take a screen shot of the screen when you see the white spot. If the white spot isn't in the screen shot, that means it's an issue with the LCD screen and it needs to be repaired. To take a screen shot, press and hold the Sleep/Wake button, then immediately press the Home Button. After the screen flashes, you want to find that picture in your Photos application and send it to your computer or someone else to have them verify if the white spot is or isn't there.
Keep us posted.