The story...

The 9/11 cell phone calls could not have been made as described

Before this new "Pico cell," it was nigh on impossible to make a call from a passenger aircraft in flight. Connection is impossible at altitudes over 8000 feet or speeds in excess of 230 mph.
http://www.nypress.com/17/30/news&columns/AlanCabal.cfm

Our take...

Much of this claim comes courtesy of AK Dewdney's "Project Achilles", where he tried making cell phone calls while flying over London, Ontario, then reported on the results.

To the extent that the cellphones used in this experiment represent types in general use, it may be concluded that from this particular type of aircraft, cellphones become useless very quickly with increasing altitude. In particular, two of the cellphone types, the Mike and the Nokia, became useless above 2000 feet. Of the remaining two, the Audiovox worked intermittently up to 6000 feet but failed thereafter, while the BM analog cellphone worked once just over 7000 feet but failed consistently thereafter. We therefore conclude that ordinary cellphones, digital or analog, will fail to get through at or above 8000 feet abga.
http://www.physics911.net/projectachilles.htm

End of the story? Not necessarily. Note this description of the route Dewdney flew in part #2 of the experiment, for instance:

For this experiment, we flew a circular route, instead of the elongated oval. The circle centred on the downtown core and took us over most of the city suburbs. All locations below are referred to the city centre and are always about three miles distant from it.

The previous experiment, called Part Two, established a distinct trend of decreasing cellphone functionality with altitude. It was conducted in a four-seater Diamond Katana over the city of London (pop. 300,000), Ontario in Canada, an area richly supplied with some 35 cellsites distributed over an area of about 25 square miles.
http://www.physics911.net/projectachilles.htm

Dewdney is making calls within a short distance of the city centre, then. It's unclear how many mobile phone base stations would be within this area, but he describes it as "richly supplied", and that would make sense. Networks must install more base stations in a populated area because each one can only support so many simultaneous calls; the higher the surrounding mobile-using population, the more base stations you need.
 
There's a consequence to this, though, as Ericsson spell out.

Each base station can only serve a limited amount of users at a time. As the number of mobile phone users grows more base stations are needed. When there are shorter distances between base stations and mobile phone users, however, less output power is needed to communicate.
Ericsson factsheet

In other words, base stations in urban areas use less power, and therefore have a shorter range, than those out in the country. What is the potential range? We couldn't find a US figure (email if you can), however a German page may offer a clue:

To serve a specific region, the region is divided into separate sub-areas (cells). These extend like a honeycomb over the entire Federal territory, but have different sizes. The diameter of a cell ranges from less than 100 metres in inner cities to 15 kilometres in rural areas. The more transmitter locations there are, the smaller the individual cells can be. The smaller the cell, in turn, the lower the broadcasting power of the individual antennae can be.
http://www.tab.fzk.de/en/projekt/zusammenfassung/ab82.htm

100 metres to 15 kilometres is around 328 feet to 9.3 miles: an enormous difference. If Dewdney were flying over base stations with a range at the lower end of this scale then it's not at all surprising that he had problems making calls. However, this does not prove that calls could not have been made from a plane flying over rural areas, where the base stations may well have used more power, and had a greater range.

We've also seen a suggestion that the phones Dewdney used may have been less likely to work than those available on 9/11. We have no idea if this is true or not, but it's a point to consider:

So attempting to make a call from a plane today using a newer technology cell phone isn't really a fair comparison. The analog system is patchier and discontinued in many places altogether; many phones only offer access digital now anyway. On 911, the callers on the hijacked craft were almost certainly off the digital network using a trimode (or lower quality) phone. When digital couldn't get through, their phones switched to analog which, at least in a 911 call, gave them a better chance of getting through.
 
This still doesn't clear up how calls were made at altitudes over 8,000 ft (and possibly up to 30,000 ft).
http://www.rense.com/general56/cellpp.htm

However, even with these issues, Dewdney does not (as many people paraphrase him) say that calls above 8,000 feet are impossible. In fact he specifically says they can (for at least one type of cellphone -- please, read the full link for clarification of this if you've not done so already):

Calls from 20,000 feet have barely a one-in-a-hundred chance of succeeding.

The results just arrived at apply only to light aircraft and are definitely optimal in the sense that cellphone calls from large, heavy-skinned, fast-moving jetliners are apt to be considerably worse.
http://www.physics911.net/projectachilles.htm

Whether his results are "optimal" is open to question, as we've seen, however here he is suggesting there's a 1 in a hundred chance of success of making a call. So how do we get to "impossible"? Like this:

As was shown above, the chance of a typical cellphone call from cruising altitude making it to ground and engaging a cellsite there is less than one in a hundred. To calculate the probability that two such calls will succeed involves elementary probability theory. The resultant probability is the product of the two probabilities, taken separately. In other words, the probability that two callers will succeed is less than one in ten thousand. In the case of a hundred such calls, even if a large majority fail, the chance of, say 13 calls getting through can only be described as infinitesimal. In operational terms, this means "impossible."
http://www.physics911.net/projectachilles.htm

What Dewdney is saying is that the probabilites must be multiplied together. If the chance of you winning a basic prize on the lottery is one in ten, for instance, then the probability of you winning twice with two tickets is 10 x 10 = 1 in 100.

When we're dealing with unrelated and independent events, like the lottery tickets, this is correct. But the phone calls were not independent, they relied on precisely the same set of circumstances. If a 9/11 plane were in the right position, in relation to a powerful base station, for the calls to take place, then it was in the right position for everyone on the plane (who had a mobile which could use that base station). At any given moment, either all this group of people could get through, or none of them. Therefore the chance of two people getting through remains close to 1 in 100, even with Dewdneys flawed conditions, not the 1 in 10,000 he claims.