In the bad old days, parsing real-world HTML was a horrible task because every web-browser had a huge collection of undocumented corner-cases and hacks; some accidental, some the result of reverse-engineering other vendors' corner-cases and hacks. Most standalone HTML parsers could generate some document tree from a given input file; whether or not it would match the one generated by an actual browser was another matter.
These days, however, we have the HTML5 parsing algorithm, reverse-engineered from various vendors' web browsers but actually documented and implementable (still horribly complicated, but that's legacy content for you). Not only is the HTML5 parsing algorithm designed to be compatible with legacy browsers, modern browsers are replacing their old parsing code with new HTML5-compatible implementations, so parsing should be even more consistent (I know Firefox has switched to an HTML5 parser, I think IE has made a bunch of noise about it too; I don't follow WebKit all that closely, but I'd be surprised if they haven't moved towards an HTML5 parser).
These days, however, we have the HTML5 parsing algorithm, reverse-engineered from various vendors' web browsers but actually documented and implementable (still horribly complicated, but that's legacy content for you). Not only is the HTML5 parsing algorithm designed to be compatible with legacy browsers, modern browsers are replacing their old parsing code with new HTML5-compatible implementations, so parsing should be even more consistent (I know Firefox has switched to an HTML5 parser, I think IE has made a bunch of noise about it too; I don't follow WebKit all that closely, but I'd be surprised if they haven't moved towards an HTML5 parser).