What’s the most forgiving HTML parser in Python?
If beautifulsoup doesn't fix your html problem, the next best solution would be regular expression. lxml, elementtree, minidom are very strict in parsing and actually they are doing right.
Other tips:

I feed the html to lynx browser through command prompt, and take out the text version of the page/content and parse using regex.
Converting to html to text or html to markdown strips all the html tags and you will remain with text. That is easy to parse.
I have some random HTML and I used BeautifulSoup to parse it, but in most of the cases (>70%) it chokes. I tried using Beautiful soup 3.0.8 and 3.2.0 (there were some problems with 3.1.0 upwards), but the results are almost same.
I can recall several HTML parser options available in Python from the top of my head:

BeautifulSoup
lxml
pyquery

I intend to test all of these, but I wanted to know which one in your tests come as most forgiving and can even try to parse bad HTML.