Also, does the neatness of your html affect how fast you page loads?
Nope. Someone mentioned that the browser might parse the HTML faster, but this is untrue. Whitespace is generally stripped out as one of the first steps in parsing HTML (or any code). Since HTML takes any amount of line feed, tab, and space as one, it makes absolutely no difference. As for download times, unless your pages are significantly affected by your extra spaces/tabs, it will be negligable. Plus, text is highly compressible, especially repeated characters.
I have a related, somewhat annoying problem. I have a bunch of files that ended up with basically just one very long line.
Make sure you upload text files in ASCII mode (or "Text" mode, depending on your FTP client). Windows, Mac, and Unix systems all have a different character (or characters) to indicate the end of a line. ASCII mode makes the appropriate conversions. Never trust "automatic" mode unless you can edit the list of text file extentions.