What can cause a single red line to app...

you have a dead row of pixles, this is a common problem in LCD screens that have been in use for a while, the line appears (it's color is sometimes different, and it is sometimes verticle [my computer has a verticle blue line]) this cannot be fixed, you can try to ignore it, and if you cannot then you need to get a new monitor.

Thats a generic problem with LCD screens. Its more common in Mobile screens. Sorry, no there is no fix to it other than replacing the LCD itself. Just pray that it shall not grow because as and when the compressed gas from within the LCD will leak the line will be becoming broader and broader. It is caused by damage to the LCD corner Just a hit on side of LCD and a hairline crack for giving way to the encapsulated gas.