First of all, good work Simon! I hope that one day the format of a particular wiki article becomes a user choice - I think your MarkdownSyntax extension is a step in this direction.
Regarding my comment that my ExtendedSyntaxParser is "not amicable to running along side certain other kinds of extensions", I'd like to expand on that a little. The reason it doesn't play well is that it uses the PHP SAX XML parser to identify blocks of markup that exist outside any tags or attributes. Unfortunately, the parser doesn't provide a way to detect and handle XML/HTML comments <!-- like this -->. It seems to just skip over them altogether.
So in order to play nice with extensions which inject XML comments into the article body, the ExtendedSyntaxParser really needs to be able to break apart the incoming text around these comments and preserve them in the output.
I hope that makes sense. It has been my intent for some time to revisit the code and figure out how to preserve the comments so that this is no longer an issue. I've been holding off releasing the ExtendedSyntaxParser here (on mediawiki.org) until I've solved that problem as I feel that it's a significant drawback to its usage.
The good news, however, is that since you're using ExtendedSyntaxParser rather than recreating the functionality yourself, when I do get around to fixing ESP, MarkdownSyntax will immediately benefit. --Jimbojw 14:23, 29 May 2007 (UTC)
Source of bugs
I suspect that the reason for the broken  links is that Markdown doesn't assign id's to any of its headers. --Anonymous
Breaks MediaWiki 1.20.2
The Fix for Mediawiki 1.20.2
I couldn't get this extension to work, so I used the Alternate Syntax Parser instead. The patch in the Comments page on the Alternate Syntax Parser works with MW 1.21. Tomjohnson1492 (talk) 05:08, 31 May 2013 (UTC)
This extension does not install properly in recent MediaWikis
After following the installation instructions and double-checking,
require_once('markdown.php') does not import the MarkDown class correctly from the other file, resulting in:
[Fri Oct 25 16:09:33 2013] [error] [client 22.214.171.124] PHP Fatal error: Class 'Markdown' not found in /var/wiki/mediawiki/extensions/MarkdownSyntax/MarkdownSyntax.php on line 89
126.96.36.199 14:28, 25 October 2013 (UTC)
Special:Version is all messed up on 1.18.1 with version 0.2, there should probably be a way not to break p and td tags. :) --Nemo 22:17, 14 October 2014 (UTC)