Press command-shift-4 and drag over an area where these glitches show. Do they appear in the screenshot or not?
I am guessing that the screenshot will not show these issues, which would suggest it is indeed a problem with the cable connecting the motherboard to the display. It is an easy fix for an Apple service provider, if they are allowed to do it... as the machine is nearly 7 years old, I'd take in sooner, rather than later. You don't want the machine added to the "obsolete" list, and then the service providers will not get the parts for it.
Another easy test, which can also be used as a workaround, is to attach an external display. In all likelihood, the external display will work perfectly - all but confirming the diagnostic suggested above.