Tonzaman, I keep thinking that maybe someone who knows what they're talking about will simply diagnose your problem. I'm way out over my head here - just a long-term Mac user willing to make guesses. I never really got around to learning all that much about OSX, in spite of some thick books sitting around that I always meant to get around to reading/remembering. Anyway, if you get good advice from someone who really knows what they're talking about, don't hesitate to forget anything/everything I'm posting now.
Apologies for the length here; clearly I'm allergic to SHORT...
Your new screenshot doesn't remind me of those I happen to remember from long ago in researching bad RAM. That probably doesn't mean much, though. In your shoes, I'd still want to rule out bad RAM if no one comes up with a software answer. I'd also want to rule out a graphics card problem if I could.
Now I understand what you mean by the volleyball problem. I saw that here in 10.8 and in 10.9 but not so often since then, and so far with El Capitan I might not have seen it at all (8 GB RAM on this iMac, so I never understood why that problem arose in the first place). When I've seen that kind of slowdown problem, it tends to occur during copying activities, including copying a few small files. (Amazing! That seems to be a somewhat *basic* ability for any computer operating system to get right before proceeding to the fancy maneuvers, of which there are plenty on El Capitan.)
Probably your volleyball problem isn't related to the screen display problems unless both are being caused by RAM that's going bad. That's easily possible. I don't think you can say much for sure about the volleyballs except that your system software is busy and isn't handling basic chores efficiently. That could be happening because of something to do with the system itself, or something to do with its interaction with your third-party applications (some of which might have some processes running in the background, whether you've turned them on or not).
I read a few more posts last night and tripped up over this bit of information: Apple does still make available either its Hardware Test utility or the newer version, Apple Diagnostics. It's sitting there on your recovery partition. I also remembered that actually what I did when using it from its DVD was to do a clean start up by holding down the D key. Then the computer started up from the DVD, automatically opening the Hardware Test onscreen. The Hardware Test/Apple Diagnostics work exactly the same way nowadays, and your computer would already have the proper testing utility on it on that recovery partition - whichever version that's appropriate for your own computer.
Maybe just spend your time now investigating the display glitches? See what happens using the normal testing levels by the utility. If nothing pops up there and you still get no answers through some continuing online research or posting at other Mac-oriented sites besides Apple's, then do the longer testing that's possible using Apple's utility.
I assume that you've already thought of the often-advised steps of resetting the VRAM (Command, Option, P, and R held down while starting up afresh) or the SMC ( <https://support.apple.com/en-us/HT201295> ). It's not a bad idea to do things like that that aren't hard before proceeding with things that are more trouble and require more time.
Once you've exhausted everything easy you can think of, then it's time to get to an Apple genius bar at the Apple Store. If that's not easy either, then you could try first to solve your own system problem. It would just consume some time and take away the benefit of having the use of your computer while you work on fixing it. (But you could be sipping tea/whatever while you work.)
If I were in your shoes and wanted to solve a system holdup problem myself, I'd be thinking in two directions, but whichever direction I took for starters, I'd begin by making sure that I had TWO fully tested bootable backups of the entire hard drive on two different external hard drives OR two fully tested bootable backups on two different volumes (drive partitions) on one very large external drive. I'd make sure that those two different bootable backups were made by two different utilities, and not count on either one of the backup utilities to always work as expected.
(Note: I have used a large number of different backup utilities, both free and expensive/very expensive and Apple's own Time Machine. My experience has been that every single one of them has failed when there was no good reason whatsoever that they should have failed. I have NO backup utility to particularly recommend, after all these years of making and using backups. But they have all worked MOST of the time.)
Maybe you might read up a bit on any extensive third party software you have on your computer. Example: I think El Capitan has a problem with Adobe's need in CS-5 and CS-6 for Java installations. Maybe the El Capitan installer should have taken it out (if you have Photoshop) but didn't. Or some sort of problem like that one with *any* application that you intentionally put onto your computer, but that perhaps doesn't play nicely with El Capitan now. If you have 400 extra applications, I can see where this would be too much of a chore, but maybe just try to get a feeling for the largest third-party applications you have and look online for other users' comments with respect to compatibility with the new system.
If that gets you nowhere...
The next thing I'd do if I were in your shoes would be to reformat the drive on your computer. (It's not a really big deal even if you've never done this.) Then do a fresh install:
Startup by holding down Command-R. Get the reformat done first by pulling down Disk Utility from the menu at the top of the screen. Erase the drive. Create however many partitions you want (maybe just one unless you're installed a bigger drive then what probably came on your MacBook Pro). Use the defaults - OS X Extended (Journaled) and GUID for the partition "Scheme." After that, close the Disk Utility and you're ready for the fresh install to proceed.
Once the system is installed, don't put any of your own third-party software back on the system yet. First check out the basic functioning of the computer running this new clean system. Take a good bit of time at this, including by copying offline your own data files like music and pictures from your backup drive - and look for screen display problems as everything progresses.
Since you'd now have a perfectly clean new El Capitan system, then use it for awhile during and after copying your stuff, remaining offline the whole time with only Apple's system as installed on your computer. After you're satisfied that you can't find any problems, then again go online, but download absolutely nothing at all. Your first uses of Safari should be in a very secure mode - don't use any Javascript or allow any cookies or internet plugins (unless it's temporary and only to visit webpages within the apple.com domain). Fix those security prefs in Safari preferences.
You're just making sure that your computer continues working fine without the complications of worrying about other things messing up your screen display. You want to see whether any screen messes show up while having just Apple's own applications running on the computer. Try using iTunes with some music that you own and keep on your own computer. Keep going with Apple's own software until you've used all of Apple's stuff that you ever use, with as little online interaction as you can get by with.
If no screen glitches appear, then you could start SLOWLY putting back some software you installed intentionally on earlier systems and need to run on your computer now with El Capitan too.
Install just one third party program program at a time, followed by a significant amount of computer use time spent with that program before following with any other additions, one additional application at a time. Include some good bit of work in the Finder while each extra third party application is added and running, even if you have to keep moving the same files back and forth between a couple of folders you create just for this busywork. When you feel certain that the program you just put back and checked out is not something causing the screen problems to return, go on to putting back the next third party application, and so on. This may wind up taking you days to accomplish.
If at the end of those days your system and all personal third-party software is running just fine, then you might assume that you somehow previously inadvertently allowed something onto your computer that was messing things up but just started to show up more clearly with El Capitan's security features working. This can happen, even if you're very careful in browsing security prefs and in deciding on downloads. Sometimes you might have a good guess at what's causing the problem (gut feeling). Sometimes not.
Maybe then you could cautiously reset Safari (and any other browsers you use) to allow what you feel comfortable with allowing on those (only on those) websites you feel secure with. The Command-comma key combination brings up the browser prefs to quickly make changes there.
IMPORTANT NOTE: If by any chance you get the screen problems back *before* adding back any of your software at all, then something about the system and your hardware isn't working. In that case, see if you can go back to an earlier system through another Command-R startup. If you can't, then go to the Apple Store to download an earlier system by searching on "Install (the name of the earlier system you want).app". Download and use DiskMaker to use that download to make yourself an installer (look in your Applications folder for it - takes a good while to download but it will automatically plops itself there once you've downloaded it). Make your installer on a USB flash drive that's formatted to OS X Extended (Journaled) and GUID for the partition "Scheme." Reformat the computer drive again and reinstall the earlier system you want off that USB drive.
Keep that earlier system installed until a few months have gone by and Apple has done some more updating of El Capitan before trying the new system again. Save your USB drive completely intact, just in case....
I'm just assuming that an earlier system would still work fine if you first thoroughly checked out the hardware with Apple's utility and everything looks good there, including with the long version of the RAM testing.
But if an earlier system doesn't work fine now either, then possibly something worse has happened to your hardware that just happened to coincide with the new system's install? Apple might be able to resolve your issues through using some additional hardware testing that is only available through an Apple authorized repair facility.
If your machine's warranty period is past, I know how hard ($$$) it can be to have to contemplate calling Apple. Very best of luck to you in figuring out what's going on now.
Mary
