I'd be more than happy to assist you. The Samsung Galaxy S III has a feature that use the front facing camera to determine if you're actually looking at the screen. The idea is to keep the screen from timing out when you are looking at it, and to save power by turning off the screen when you're not.
Like all new cool things, it doesn't always work as planned. Your only real option here is to disable the feature.
If you'd like to learn more about the feature click here: http://www.samsung.com/global/galaxys3/directcall.html#smartstay
This is really odd. Could it be you're covering up the proximity sensor? I say that because you mentioned headings which is at the top of emails and the top of the phone is where the proximity sensor is, typically behind the tinted area of your GSA glass. The GSA is a new phone and I know Samsung likes to tweak things so follow my instructions below, the wording I use my be slightly different in Samsung's implementation the general idea/principle is the same.
Go to settings
Then go to Display or Screen
We want to disable the screen going blank IMMEDIATELY and change is to something like 45 SECONDS
That way assuming you have big hands and you're inadvertently covering up the proximity sensor, the screen wouldn't go to sleep immediately,
My problem still not solved. Just to make it clear:
1, This does not happen in any other function of the S3.
2. When an email comes in, I click to open it and then click on a subtitle in the email (where applicable
3. The email will then open and at the same time the screen goes really dim, almost unreadable
4. I am Android literate - S1, S2, S3 and Galaxy 7.7 tablet, custom roms, rooting etc so I do understand what you are advising
Go to Settings
Select Applications or Apps ->All
Select Manage Applications
Select Force Stop and Clear Data
Go back to ALL and select Google Services Framework
Select Clear Data.
Turn your device off and back on.