I suspect the first point is due to a known bug, that only occurs if your dates are not US format.
The slider shows, e.g. 1/6/2013 = 1st June 2013, but it is actually being processed as 6/1/2013 = 6th Jan 2013.
This is slightly confused by the fact that the issue only exists on Server, so it works fine when you are designing it!
The only solution at the moment is to use multiple parameters/filters for year, week, month etc.
A highly annoying issue for those of us not US-based!