g1smd - 7:05 pm on Jun 25, 2013 (gmt 0)
If you re-include Rule 3 it should instead redirect both .html and .htm requests to extensionless. If you have no pages which map old to new URLs simply by removing the extension then you probably don't need this rule. However, I'd leave it in simply in case someone does ask for one of your new pages but for whatever reason adds an extension to the URL request. A slightly modified Rule 4 could achieve the same result.
The code in Rule 6 doesn't match the plain-English description in the comment. As coded, the first RewriteCond stops the redirect when any of the www. or ftp. or mail. sub-domains are requested by HTTP. Is the comment what you want to do and the code wrong, or is the code right and the comment wrong?