The hotter your GPU gets, the more trouble it has creating 3D images. Under load, when you start seeing artifacts (the dots and lines you've noticed) it's most likely because your card is running too hot. This can also cause random restarts and freezes, like when your PSU, RAM, or CPU is running too hot.
Download
Speedfan , a small utility to measure system temperature (among other things). Your processor temperature should not exceed 55 degrees Celsius. Your GPU temperature should not exceed 75 degrees Celsius. Make sure all your case fans are running at 100% speed.
You didn't provide any information about your system. But, if you have dedicated graphics (a video card on your motherboard, rather than a chip built into your motherboard that processes your graphics), then download
Rivatuner, a utility you can use to unlock higher fan speeds on your video card. Set your video card fan for 100% speed.
If your GPU is still running too hot, pop the case open and blow a fan directly onto the video card when you are going to put it under stress. A more permanent solution is to buy a larger case, buy a
heatsink your video card.