Fixed capitalization of headers per MoS:  there was more than one incorrect.  Beyond that: 
 * Didn't explicitly add Sephardic/Israeli because that is reflected in the article title.  That isn't obvious? (That's a real question, not a rhetorical one.) 
 * Let's discuss the Reform stuff after 9 Av.  I know this is a hot button for you. From a WP:NPOV perspective it can't be omitted, and I thought the current approach was nice and compact. But I'll welcome your ideas on how to handle it differently, as long as it appears somewhere. 
 * Let's discuss "dual nature" after 9 Av, too.  I could rewrite that sentence without the phrase along the lines of "The idea that Shemini Atzeret is part of Sukkot in some ways and apart from it in others is reflected in the observances and customs of the day(s)", and it wouldn't be WP:OR.  It would clearly be a summary of the preceding, plus a transition to the next session.  Possibly the phrase "dual nature" suggests OR, but I see it simply as a neater package for the idea. 
 * I included the Vilna Gaon because I thought the preceding quote from the Gemara (about akh sameakh) needed elucidation.  Does it work better put together into a single paragraph?