There is indeed a profound question regarding the thermodynamic state of the universe, and its relation to entropy. Ironically, though, ID'ers seem not to be aware of it, and instead use incorrect arguments about the "entropy of life."

The facts are these: "Phase space" is a way to express the state of any system. The state of a system corresponds to a point in phase space -- the location of this point in phase space tells you, for example, the velocities and position of every particle in the system being studied.

In thermodynamics, we take all the states that look approximately like one another (they are described by the same "temperature" and other macroscopic variables) and note that all these "similar" states occupy some region of phase space. Phase space is thus divided up into many regions, each region describing a seperate thermodynamic state.

The entropy of a particular thermodynamic state is the log of the volume of the region in phase space it occupies.

With that background, one can do a quick calculation. Using the Bekenstein-Hawking entropy formula for the entropy of a black hole (a high-entropy state), one can approximate the total phase space volume of the universe by putting all the matter in the universe into a single black hole. This gives a phase space volume (in any reasonable system of units) of about 10^10^123. This is a simply enormous number -- it represents the number of possible states of our universe.

Then, one can look at the current thermodynamic state of the universe, and estimate its current entropy based on the big sources like the black holes at the centers of galaxies, the cosmic background radiation, etc. and determine the volume of phase space that corresponds to our current state. One obtains an estimate of something like 10^10^101.

Now, this is interesting, because 10^10^101 is absolute chicken feed compared to 10^10^123. In fact, divide the latter by the former to find how "generic" our universe is, and one finds that to get a universe that looks anything at all like our universe, one must specify the state to one part in 10^10^123 (i.e. 10^10^123/10^10^101 = 10^10^123).

Now, this is rather incredible, because statistical mechanics is based on the notion that there is no "preferred" region of phase space -- they are all equally probable. This means that ordinary statistical mechanics predicts a universe like ours (that is, one in which all the matter is not down black holes, which would apparently be far more probable) with a probability of 1 in 10^10^123.

As everyone is probably aware (and someone is sure to bring up), there is a thing called the "anthropic argument" which says "the universe appears special because we require a special universe to be alive in order to observe it." Interestingly, this does absolutely nothing to diminish the above argument -- a universe dominated by black holes, except for a single galaxy to support life occupies a far, far, far, far greater region of phase space than our universe does, and thus is far, far more probable than the universe that we observe.

So anyway -- yes. There are some profound puzzles regarding entropy and the thermodynamic state of the universe. Our universe appears to be fantastically special (in the most genuine sense of the word), given our understanding of statistical mechanics.

There is an online lecture (by Roger Penrose) on this stuff here: http://www.princeton.edu/WebMedia/lectures/
Lecture 3 of his series deals with entropy and cosmology.