It's interesting to note that applying the second law of thermodynamics to the whole universe, even if we didn't know about expansion, yields one of the biggest disconnects between prediction and observation since the ultraviolet catastrophe. If the second law applied to the whole universe, we should expect the Big Bang to have been quickly followed by a heat death. Having the entire universe we see today become so extraordinarily well organized from an initial glob of hot uniform plasma would have an inexpressably small probability. It seems far more likely to say that, for as yet un-determined reasons, the second law can't apply to the universe as a whole, only to certain subsets of it.

Might also suggest that the problem of black hole entropy is not actually settled, and that black holes could in fact simply reduce entropy instead of emitting Hawking radiation.

Also, it's interesting to note that expansion of the universe actually "breaks" the first law of thermodynamics: energy is not actually being conserved, new energy is being created. This can happen because the first law of thermodynamics only applies in a fixed size space, while in the expansion model we believe that space itself (the coordinate system, as it were) is expanding.