After an private exchange on Apache Mailing, I post my problem on the Ubuntu list.
Apache crash randomly and returning Error 500 (Premature end of script headers).
I was ubuntu 10.04 and I never problems (Apache and PHP are compiled, I do not use APT).
I upgraded to Ubuntu 12.04 and Apache randomly returns errors 500 when I load a PHP page.
Here is a STRACE when it does not work:
http://pastebin.com/mNw9v4SR
Before migrating from 10.04 to 12.04 I've compiled PHP 5.2.16.
After the migration I've have compiled 5.2.17.
If I use PHP 5.2.17 Apache have random errors.
If I use PHP 5.2.16 Apache have never error.
In summary, all new compilations give random errors (PHP 5.2.X, 5.3.X PHP, PHP 5.4.x).
In de STRACE when Apache return a 500 I see many "unfinished":