Yes, it is possible for HDMI or Dispalyport to misbehave. I have first hand experience with it. I even saw BSOD due to incorrectly inserted DP cable. The latest thing I saw was flashy pixels in the top left corner of a high resolution, high refresh rate screen.
In any case, try playing with the display output's timing. It is different places for different manufacturers, for example the nvidia control panel. Try reducing the blank if the display supports it. That should reduce the pixel clock, and increase the settling time for the signals. Also, make sure that the video card is not misbehaving. I've seen one, which had probably memory fault, and it was putting orange pixels in windows everywhere, and funky textures in 3D applications. Make a screenshot, move it around, see if the errors follow the picture.