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I think I will change all links to my home page to :
[mysite.com...] as they now point to .html
I want to avoid duplicate content penalty, so I hope perhaps if I re-shuffle my home page to look different, would it help?
This effect is easy to see if you use Xenu LinkSleuth to check your site. You see the list of URLs is twice as long as expected, and half of them have a title of "301 Moved Permanently". This will cause you a lot of problems.
Always add the trailing / to folder URLs.