I am getting kind of desperate with this problem. When working on Word 2011 documents, my computer sometimes starts typing squares on its own. It may stop after a few lines but most of the time, I have to click with the mouse several times or simply save file and exit. This behavior may return after quitting Word. I have changed the mouse to the new Magic 2 from Apple, and removed the USB extension cord that connects the keyboard to the computer, also switching to another USB computer port. Additionally, sometimes on the desktop or in Outlook I click on an item but the highlight does not occur staying on some other icon. Relaunching Finder helps temporarily. I am on the latest El Capitan (11.2) and working on a MacPro 2010. All tests of the computer come out with nothing wrong. Restart does not help. All key options in the Accessibility control panels are unchecked. Internet forum search came up with some similar issues but no good remedy was suggested. Have no idea whether this is software or hardware issue (like old wired keyboard). Suggestions are much appreciated.

Have you tried logging in to a test user account to see if your issues follow you, Alex?

And this is a bit of a stretch, but although I'm not sure about empty squares, I know that squares with an "A" in them indicate a font issue, so a safe boot to clear some caches, perhaps an even deeper cache clearing, may be helpful.

Thanks, Artie! Will do. Maybe not a stretch after all! Did not really think about caches because it is not abnormal characters, but a free typing, like in some movies when the computer is hacked and someone types in front of your eyes without you touching the keyboard. Exactly like in the latest Stieg Larsson's novel ))

might also want to try to locate another keyboard to test out in those circumstances, as well as unplugging and replugging the keyboard. I keep Keyboard Viewer accessible in the menubar for just such situations, so I can see if I have a stuck key or something. Has your keyboard suffered a liquid spill recently?

Keyboard Viewer can vary slightly in its location depending on your OS. You turn it on using system preferences, keyboard, international. It's one of the top language options, and when selected will cause the input menu widget to appear up in the toolbar near the clock. Access it from there when you want to see precisely what's going on with your keyboard. I've used it many times to diagnose stuck keys, often caused by liquid spills.

I haven't seen the squares in a long time — maybe since Apple went to 16 bit character sets. Those generally indicate ASCII characters that are not in the font currently in use. They may be showing up in Word 2007 because of the font in use or Word 2007 does not fully apprehend 16 bit characters. The real question, of course, is what is throwing those characters?

V1 has already suggested a good method for testing stuck keys, but the mouse behavior leads me to suspect issues beyond the keyboard creating spurious USB input signals. (Remember, Bluetooth is seen by the system as a USB connection.) So in addition to the keyboard I would look at…

• Any and all USB devices including hubs and connecting cables.
• Any third party USB drivers you may have installed such as USB Overdrive.
• Any device with Bluetooth active that is within 30 to 45 feet of your computer even if they are not paired with your computer.
• Look in System Preferences > Bluetooth for any paired Bluetooth devices — active or inactive — you aren't using or don't need.

Thanks, gentlemen!
I started by following Artie’s advice and used Onyx to purge all the caches, then ran the FontBook that validated all fonts. Removed a couple of duplicates. The behavior returned, unfortunately. Also annoying is that in Outlook you want to click to one item but the highlight is kept on the newest one on the list. Shaking the mouse remedies that for some time. Could be a bluetooth problem actually, although my keyboard is wired. At home I have a brand new iMac 4K which also has some weird behavior in Word. Very often the word highlight does not work when the cursor is dragged left or right. Shaking the mouse allows proper highlighting. This is why I suspect Bluetooth. Will try to delete Bluetooth preferences.
Then tried to work out of the test admin account and all seems OK, although did not used it for long. Looks like mostly (if not always) the Office is affected, although never had a problem with PowerPoint text. There is an update to office released recently. Will apply it, maybe it would kill the problem.

Virtual1, thanks! I have now put the keyboard viewer on the desktop to see if there are any sticky keys if the square typing returns.
P.S. Have no spare keyboard yet. My son loves his Logitech solar Bluetooth keyboard that is very accurate (model 760); it also allows toggling from computer to phone to iPad with one button. I am considering that one if I find that keyboard is bad (5 years old but no spills).
P.P.S. In the Bluetooth prefs I have just one mouse showing.

Could have been a software issue. After Office 2011 update to 14.6.0 that came yesterday, Word seems to behave.

Update: the behavior returned. This time the keyboard viewer was on the desktop. No keys showed up as depressed while the squares were being typed. Shaking the mouse stopped the typing. This shaking also helped stop erratic mouse behavior in Outlook where only one item could be highlighted but not any other one. I will delete mouse preferences and then give up...

That shaking the mouse thing is weird; have you swapped it out?

And I hate to suggest it, but the tried and true remedy for Word ills has been reinstallation.

The mouse itself can produce keystrokes, it's a USB device. There may be a hardware issue / defect / failure in the mouse itself. Specifically if shaking the mouse stops it, I'd strongly suspect a defective mouse. Could be fixable by an electronics repair person (cold solder joint) Could also be due to low batteries, known to cause random malfunctions.

There's also a very remote possibility something is interfering with the wireless signal, another nearby device operating on the same frequency?

The mouse is brand new. The old one behaved in the same way. The same thing with shaking the mouse happens in a 3-months-old iMac when the word highlight in Word does not work. Could be a weird Bluetooth issue…
Ordered a new wireless keyboard from Logitech (the existing wired one is over 5 years old).
It crossed my mind to reinstall Office. Maybe I would do that if the new keyboard does not help. Actually, our place offers Office 2016 for 10 bucks (no Cloud, just standalone).

On a general note, I found a blog of a person who had Bluetooth problems with erratic mouse behavior on an iMac under El Capitan. His latest update was that some problems may be a result of a Handoff feature enabled in General preferences. His advice was to uncheck the “allow Handoff between this Mac and your iCloud devices” and restart the computer.
Will try to do it and see if this helps.

Update. Changed the wired keyboard for a wireless Logitech 760. The erratic behavior with inadvertent typing seems to be gone.