There are a few incompatibilities between Apache 2.2 and 2.4. These are described in detail in the Apache 2.4 documentation.
In most cases, the source of compatibility problems is an .htaccess file. If it is not compatible with Apache 2.4, it will cause your site to return "500 Internal Server Error."
To narrow down the specific cause, we recommend that you enable your site's error log in the member interface (if you haven't already). Once it is enabled, access the site a few times to exercise the error, and then the error_log file in your site's logs directory should point you directly to the problem.
The most common example comes from using the Order directive to restrict access to certain content. It has been completely removed from Apache 2.4, but is still very common in example files and configs distributed with many web applications that haven't been updated yet.
To update a 2.2 .htaccess file containing something like:
Order deny,allow Deny from all
the 2.4 equivalent of both lines would be the single line:
Require all denied
to deny all access and:
Require all grantedto allow it.
Other 2.2-specific configuration directives that have changed in 2.4 can be similarly adapted. See the Apache documentation linked above for complete details.