I swear, I looked thought about this for about twenty minutes trying to find an alternative before I actually tested it to replicate the problem. I think I found part of the problem. All the areas that should have "<?php" or "?>" instead have "&lt;?php" and "?&gt;" which your processor can not interpret.

However, because this code is not passing through the PHP parser at all, the MIME type from the server is incorrect, which causes problems with Firefox. I would recommend rechecking the PHP script, and then have your host check the configuration settings. I have seen some hosts, for example, lock the AddType method to prevent users from mapping .html files to the PHP processor. This does not seem to be the case, however, as the MIME type I get from the server is in fact application/x-httpd-php. However, I don't think that is the type that the PHP processor is mapped to on the server. It is possible that some other type has been assigned to the PHP handler.

If all else fails, you could try the following code:
AddHandler php5-script .html

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