What can I do about frequent beach ball Safari and other apps? I very frequently get the beachball and occasionally the wristwatch (as in every minute or so if I'm using the machine multi app) as I use my Mac. This appears in all apps, especially Apple core apps. This most often happens in Safari, but can happen unpredictably in anything. It's not reliably reproducible, though doing almost anything in Safari will soon create it.

Usually, it happens when either I or an app do something (vs it just sitting there). Neither cpu nor memory appear overloaded in Activity monitor when this happens, (though just occasionally cpu goes to 100%, and fan goes full.)

System is MacBook Pro 2.7GHz Core i7, 4GB 1333 MHz DDR3 (factory spec) running OS X 10.7.4. One probably totally unrelated oddity is that the s/n of the machine never comes up on the Apple database, always apparently missing a digit in the middle. And yes, I bought it from Apple!

Solution attempts: 
Extensive.
Machine has been back to Apple, who replaced system board and hard drive.
Repeated visits to Genii (Genius's?) who have spent much time deleting, and reinstalling individual apps, fiddling with plists, general fiddling, reinstalling the OS (Clean reinstalls - as in reformat HD).

But the problem comes back, every time.

I'm not reinstalling any of my 3rd party software, as I can't bear the repeated process, but also so as to eliminate that possible source.

I'm at the end of my tether, almost can't bear to use the machine (which is NOT how I want to feel about my Mac), and can't afford to replace this still very new machine.

Diagnostic questions will be gratefully received. I would be delighted for any possible solutions.
Once I got something similar after a Snow Leopard upgrade:  spinning bechball when starting Safari and making Safari inoperable. Turned out it was an incomaptible SIMBL plugin from before the OS upgrade.

If you already replaced the motherboard and hard drive, there's really not much "hardware" left that can be eliminated.

If you already have done a clean install as well, there is really no other "software" eliminated either. Make sure you've done a total clean install though: format HDD, install the base OS without iLife, etc, DO NOT restore anything from you backup afterwards, DO NOT use your regular username and DO NOT enter your Apple ID at first boot. Do not restore and data from your backup, especially not /Library and /Users//Library

I guess I'd also try to install a different version of OSX (downgrade or upgrade, doesn't matter) and see if the problem persists.  Also try booting a different OS (Windows, Linux, boot from a Linux live CD/usb would be the easiest option). Booting in a different OS is the best way to find out if it's a hardware issue or software.

Generally a spinning beachball are caused by CPU/memory/disk access spikes, but it can also be some other kind of blocking I/O (e.g. network, USB). Maybe it's compatibility issues with your home network? Use it on a different network, try connecting to the network with an external USB ethernet adapter.

Hope that helps.