Why is there a stain on my screen?

There are a few possible causes for this. The first is the glass was not fully clean when the LCD display was manufactured, or when LCD & cover glass was assembled into the lid assembly.

• If it's LCD you'll need to replace it.
• If you can tell if the stain is on the inside surface of the cover glass you could take the cover glass off to give it a clean
• If the stain is on the top surface of the LCD you could try cleaning it (use extreme care as you can damage the screen with to much pressure)
• If you have a very dirty environment you can get ultra fine dust & smoke particles to get caught between the LCD & cover glass sandwich as well.

In these cases its often something you'll see within the first year of use. Frankly, the amount of work to even pull the cover glass off and the left over markings from doing it make this a tough call. If you've never worked on removing the cover glass on a MacBook Pro you might want to just bite the bullet and replace the complete lid assembly. While more expensive it's a lot less work and something a first time DIY can do (see below).

The other possibility is a pressure stain. What happens is something heavy was placed on the lid and pressed the LCD causing the gap between the two glass sheets to be squeezed so the LCD fluid to be pushed away causing the light to not bend as much as the rest of the crystals. Sometimes the glass is fully touching causing a black spot sometimes its just a wipe like this.

The last possibility is the crystals built a bit of memory causing them not to return to the fully relaxed state. This can happen if your background image is very contrasty (burnt image). So you may want to see if you had a graphic that has a shape that has the same outline as your stain, Apple also had a bad run of displays where the LC material the display maker used had containments but its too late to get this fixed by Apple. This also showed up quite soon as well.

You're only hope is replace the display. Here is the IFIXIT guide you'll need to follow: MacBook Pro 13" Unibody Mid 2012 Display Replacement and this is the full lid assembly: MacBook Pro 13" Unibody (Mid 2012) Display Assembly - Apple P/N 661-6594

OK, here's what it will take to get the cover glass off: MacBook Pro 13" Unibody Mid 2009 LCD Replacement pick up from Step15 following the above guide. A common issue many people encounter is they melt the rubber gasket or break the glass in the process. Which is why I don't think you really save here after you add in the costs of the needed heat gun, replacement gasket and the possibility of needing a new cover glass, and if you don't damage the LCD as well (penny wise, pound foolish).