I agree with your first point, but I'd also extend that to the second one. I think a cover should always differ from the original, at least somewhat, otherwise what's the point (at least for a single, if it was just being played live then that's different)? For example, Green Day's cover of I Fought the Law: note-for-note copy of the Clash's version (which differed greatly from the original, not sure who it's by). They released it as a single, it got tons of radio play. Respect or no respect, what was the point of that? People could've just listened to the Clash version, releasing Green Day's as a single was a shameless ploy to make money.

Covering a Who song is fine with me, but I thought Limp Bizkit's version blew (not for being different, just for being low in quality).

They released "fought the law" as a single? What album was it off of?

Apparently Jimi Hendrix played the entire Sgt Pepper album live 3 days after the album came out.

I don't think it was off an album. I figure it'd have to be a single, since I remember hearing it around school, on the radio, and everywhere else, and not being able to tell any difference between theirs and hte Clash's.

Yeah, I heard that too. I heard he played the song Sgt. Pepper's Lonely Hearts Club Band the same day it came out.

I was referring to classic originals.
Personally I think any cover version by a new or up-coming band, of an established classic, is nothing less than an insult.
Unless of course it blows the original away. Which, lets face it, is rare to say the least.

The music should be played as a tribute (a tip of the hat) and played as the original artist intended.
If I was a painter I wouldn't attempt to re-paint Van Gogh's sunflowers.

I do see the point your making, but my point is, show respect to the original.
Anything less is nothing short of arrogance.