iPhone 4 (and 4s) won't take a screen shot. What should I do?
Numerous people have reported the problem above and, unfortunately, this is being caused because you are instructed to "release both the power and home buttons at the same time."

Releasing two buttons at the same time, at computer processing speeds is impossible, so this could be problematic for some of us.  However, I have discovered that if you follow the mechanism outlined below, you will be able to always take a screenshot.


Press and hold the power button.  
Tap the home button.  
Release the power button.


Your screen will flash, and your image will be saved to your camera role.  This is effectively the same operation as you are instructed to do on every HOWTO page on the internet.  

However, if you were releasing the power button a little faster than the home key, you were preventing the operation from taking place.

UPDATE

After reading stuffe's comment on Ryokuchasan's answer, I decided to test out a few different way's of pushing these buttons and seeing if I could take a screenshot.

It turns out,  The following operations all produced a screenshot, in addition to my instructions above.

Option #2


Press and hold the home button.
Press and hold the power button.
Release the home button.  (Image is saved)
Release the power button.


Option #3


Press and hold the power button.
Press and hold the home button.
Release the power button.  (Image is saved)
Release the home button.


It was the fourth, and final means of attempting this that has failed.  See below.


Press and hold the home button.
Tap and release the power button. (iOS locks the device)
Release the home button.


This may be a bug, or intentional.  I think what is going on is that myself, and numerous others have been 'tapping' the power button, while holding the home.  I know this answer is a bit overkill but I think it's worth documenting the full observation of this issue for reference.

UPDATE #2

Great news!  Since iOS 7's recent release, I recalled this problem.  After loading the OS, I attempted the fourth method, outlined above, that wouldn't work.  In this case, iOS took the screenshot and did not lock my device.  Apparently this was a bug and it has been fixed.