Why is the expansion of the universe accelerating?

I started looking around a little bit to figure out what is the empirical evidence that the expansion of the universe is accelerating.

Reference 1

http://www.astronomy.ohio-state.edu/~ryden/ast162_10/notes41.html

If a plot of distance as a function of recession speed has a shallower slope at large recession speeds, then the universe was expanding more rapidly in the past than it is now. If a plot of distance versus recession speed is steeper at large recession speeds, then the universe was expanding more slowly in the past. (This verbal description, I realize, may be a bit confusing; a look at Figure 28-17 of the textbook should make things clearer.)  : Universe (sixth edition) by Roger A. Freedman and William J. Kauffmann III (W. H. Freeman & Co., New York, 2002)

Reference 2
http://www.youtube.com/watch?v=55pcpTjd3BY&feature=related
At minute #30:00 there is a graph showing that the expected feature of the standard cosmological model is in the opposite direction.  Instead of getting a higher redshift as they look out at further supernova, they are getting a lower redshift.

If I am understanding everything right, the supernova data turned out opposite the way they should have expected if the Standard Model is correct.  I think, though, if they really took a look at Milne's Model, they would find a much simpler explanation for the data that they have.