"To estimate the energy required to move freight by plane, per unit weight of freight, ...then [a 747's] transport cost is 0.45 g, or roughly 1.2 kWh/ton-km. This is just a little bigger than the transport cost of a truck, which is 1 kWh/ton-km....
"...This is a bit more efficient than a typical single-occupant car (12 km per litre). So travelling by plane is more energy-efficient than car if there are only one or two people in the car; and cars are more efficient if there are three or more passengers in the vehicle."
http://www.inference.phy.cam.ac.uk/withouthotair/cC/page_275...
The original article is pretty bad; the answer to the title's question, "Can we build a more efficient airplane?" is nothing but a link to MacKay. The rest of the article entertaining lead-up fluff.
For example, an airplane with a 40:1 L/D (done in the 70s, easy today) able to carry half its empty weight in payload (nothing too hard there) will require about 0.3kWh/mile per ton of payload to maintain level flight. Even accounting for propulsion inefficiencies, that's way more efficient than the 747.
Why don't we have such airplanes? Not because it's somehow physically impossible, nor even technologically impossible, but simply because it's not worth the tradeoffs. Nobody cares about increasing the efficiency of air travel if the result is an airplane that's ten times slower than a modern airliner.
Can we build a more efficient airliner? Of course! To say "no" is to imply that modern airliners are optimized for efficiency above all other things, which is pretty much ridiculous on its face. Can we build a more efficient airliner while still keeping all the other stuff we want out of airliners, like a mach 0.8 cruising speed and global range? Well, that's a bit harder.
See http://en.wikipedia.org/wiki/File:Drag.jpg for the different types of drag on an aircraft (the 'pushing stuff through the air' drag is called parasitic, and the 'side-effect of lift generation' drag is induced).
The problem is that by doing this, you increase the structural mass of the wing for a given lift as you need a longer wing. There is a point on the optimisation curve between increase in efficiency from AR & the increase in structural weight from longer wings. Boeing and Airbus have teams of people who do this stuff for a living.
There are also human factors involved, like airports being set up for a maximum wingspan, and people being unlikely to choose an airline with slower flights.