This issue is caused by network latency rather than any graphical issue. While Diablo 3 is unable to contact the game server, everybody else will seem to stand still (as your game is receiving no information saying that they're moving).
This could be caused by your internet service provider in that your internet connection temporarily stops sending or receiving data, it could also be caused by your local network - for example if you're using wireless you could be using a wireless channel that has a lot of contention or a dodgy network cable if you're wired.
It could also be caused by Diablo 3's game servers, although if this was the case it would be affecting a lot more people than just yourself.
In order to diagnose this issue I would try some of the following;
- How can I see my latency/ping in Diablo III? - hovering over this will show you your latency in MS - high numbers (300+) are bad, low numbers are good.
- Does this problem occur in any other multiplayer games? If it does, this rules out the issue being specific to Diablo 3 and will get you looking at your own network and that of your internet service provider.
- Use an online service like pingtest.net to determine the quality of your internet connection. Note that any results from this could also indicate that your local network is at fault (as it communicates with your computer) but anything shown on a service like pingtest.net will demonstrate that the issue is not with the game(s).
- If you connect to your router using WiFi, have a read through this article, which explains how to determine which WiFi channels have the most interference. If your current WiFi channel is in use by many of your neighbours, change your router to use another one that isn't as full. Interference will cause random latency and connectivity issues if you're using WiFi.
- If you have any other network devices on your network (other computers, tablets, smartphones, etc) ensure that they're not periodically checking for emails, updating Facebook apps, etc by removing them from your network completely for a period of time.
- If you're using an Ethernet cable to connect to your router, change it for another one and see if this resolves your problem.
If you're still having problems after trying these suggestions, I would personally contact your internet service provider and get them to have a look at the problems you're experiencing.