My Mac displays some glitches Sometimes my Mac Mini, plugged to an LG IPS screen, display some Glitches. For example, times ago, in my Launchpad appears these glitches:

  

To solve these glitches I had to restart the Mac.
Now in my Safari's Top Sites there's this: 


(all these glitches were immortalised with screenshots).

However sometimes, when I wake my Mac from sleep, all the screen appear with a green tint, in that case, taking a screenshot, it appear without issues and, to solve the issue, is enough just put the Mac in sleep than wake it up again.

I can't understand the cause, Apple's Genius says that, for him, is the HDMI cable, my scare is that the trouble is the GPU because my AppleCare will expire soon... For you where is the problem? Are there some test to do?
If the Genius said that the problem is in the cable, you should try swapping the cable.

With that said, TEST YOUR GPU NOW. If there's indeed a problem, you really want to get it fixed now.

Run Apple Hardware Test (if you computer was released before June 2013) or Apple Diagnostics. Make sure that you run the relevant tests. Run some sort of GPU stress test like Unigine Heaven. If anything seems to be triggering errors, bring it to the Apple Store and try to get them to replace it. GPU replacement is expensive and you'd be much better off having Apple pay for it than you.