Double quotes indicate a search expression instead of a literal. I haven't actually done any relevant testing, and I'm not convinced the difference is large enough to detect anyway, but I suspect that search expressions are marginally slower. So unless you explicitly need a search, such as when you're looking for greater than a specific value, I'd use single quotes. That shouldn't make any difference with whether it works or not, though.
The problem may have to do with your Date field's format. By creating a list box, I could see that sometimes it is formatted as a date, and sometimes it is formatted as a number. Set analysis isn't smart enough to convert formats when doing the comparison. I would suggest formatting all of your Dates the same and giving it another shot.
