Those errors are just for the homepage, albeit, there may be much less (once a tag is left open, it tends to really confuse the validator). I'd clean up the whole site for good measure; I'm a big fan of SEO PowerSuite's on-page tools when doing this sort of thing.
The line breaks don't all need to be totally replaced, the big gaps at the top just seemed a bit excessive. That particular recommendation is just based in my own superstitions, and those of others, but is based on this: the first 1/3 rule comes into play so much in SEO (weighting content placed high on a page, early in a tag, etc.); condensing the header section to a more sane level seems sensible. Some SEO auditers, such as WebCEO, will also yell at you if your TITLE tag doesn't immediately follow HEAD, for what I'd expect to be a similar thought; although again, not as scientific of a claim to my knowledge as valid code (which absolutely matters).