I see the Carter Doomsday argument is not receiving much credence here at this point in time; funny, because last time it was discussed it did have a few supporters.
The most debatable point about this argument is the fact that it assumes that a person living now has no special place in the sample of all humans who have ever lived and will ever live; a kind of argument of Copernican mediocrity principle with respect to our position in a population of unknown size.
But our position in that population is not chosen at random; we are alive at the exact period when statistical maths develops to the point where predictions like Carter's can be made for the first time. This coincides with the period when the population is rising out of the long slow growth of the pre-industrial age towards a much more densely populated developed civilisation; a change which is still in progress. I think it is safe to say that these two periods are more likely to coincide than not; an increase in mathematical knowledge is bound to accompany a successful indiustrial civilisation.
In other words, as Robin Hanson has said,
All else is not equal; we have good reasons for thinking we are not randomly selected humans from all who will ever live.
See this wiki page about the arguments for and against this concept;
http://en.wikipedia.org/wiki/Doomsday_argument