Magento only checks PHP version, and if its lower than 5.2.0 the installation process is blocked.
I think Magento should also check for extensions.
There are a few (or more than that) that don’t have all extensions on server (specially mcrypt).
I’ve created a small script that checks the php version and some extensions (a think the ones Magento needs but no official confirmation).
The script then tels user if the server can run Magento, and if not, shows the problems.
I think Magento should release something like this so we can check the server before upload the files.
This is the extension list i check
$check = array('mcrypt','ctype','pcre','pdo_mysql','gd','iconv','simplexml','pdo','dom','curl');
Some are a Magento dependency and others ZF.
Uncompress the file a upload check.php to the server and then run it