I don't see any issue with correcting broken links or grammar/spelling errors, nor do I see any issue with more significant stylistic changes if the meaning stays the same. Sometimes I add content, but when I do so, I make sure to clearly identify that it was added after the original and mark the date it was added. If it really concerns you, perhaps you could keep the original and tack it in at the end as a footnote, so that that history is kept and can be reviewed. That sort of thing is one of the huge advantages of online content.
Honestly though, I am not sure anyone has the definitive answer. The online blog format, and the ability to publish your own content, receive comments, have dynamic links, and edit your own work, is all pretty new. I think everyone is still working out best practices. The fact that you care probably puts you above the curve.