Haxies - they are programs from Unsanity software development company, and they do various user interface adjustments. They were pretty popular in the early OS X days . Because of the way that the Unsanity Haxies (such as APE-Application Enhancer or FruitMenu) tie into the system at a low level, they are sometimes thought to involved in some of the weird system behaviors people get from time to time. (Some people love their apps, some think they are bad...)
If you have any items with the unsanity or haxie word in their title, or named as per their product apps list, it would be best to uninstall those. (a list of their programs is at: www.unsanity.com/products, as well as uninstall instructions)
Director Docker and HP IO are parts of the massive software support apps that get installed when you install HP printer drivers. (Note that different HP Printers, and different versions of their installation drivers install different things, so not every computer with HP printer will have same items on it... )
It is rather likely those items are not needed, even if you have an HP printer, so could be disabled at least temporarily.
But here is the thing with Mac Login items - while you can disable it by highlight then select the "-" minus button to remove it, there is no easy way to temporarily take it out then put it back.
So I always take a screen snapshot (Cmd-Shift-4) of just the login items BEFORE I disable anything. That way, if I want to put it back, I have a snapshot to let me know what named item to go search for.
If you have no HP printer attached to the Mac, you definitely do not need those HP items.
That would also indicate the computer was setup for someone else before you got it.
I did not ask before -- is this a Used computer that was originally set up for someone else and you bought/got it to use for yourself?
If so, then there may be a bunch of stuff in there which might cause issues down the road. If so, this would begin to look like a good case for OS re-installation, to clean out old, previously installed things that now have no usefulness.
Also, perhaps it is related to flakiness in the keyboard, with the f9, f10, f11 keys? Since those keys control the expose actions, if the keys are flaky, and the computer thinks they are being pressed often, then the screen would blink in and out seemingly on its own.
TO test this possibility, you would need to temporarily disconnect your keyboard. Either just see if the expose stuff stops or doesn't happen with no keyboard plugged in, or if you have an alternate keyboard, try using it and see if the expose weirdness happens.
Did you try the new admin user test I mentioned before?
Please try each of these investigation requests, then post back with the results, as, for example, use this list:
1) i found or not found any haxies, removed any found ones, did that improve expose problem?
2) took out HP items, restarted, did that improve expose problem?
3) this is or is not a used/previously owned computer so may have strange things in it?
4) i unplugged the keyboard and/or tried a different keyboard, did that improve expose problem?
5) i setup a new admin account, restarted into that user, did that improve expose problem?