The main reason I'm skeptic about IQ has something to do with degrees of freedom, as used in physics. It doesn't sound possible that you can describe something as complex and multi-dimensional as the human intelligence using a single parameter.
Even cars, which are a lot less complex than the human mind, cannot be described with a single parameter. There's no such a thing as a Car Quotient, nobody calls a dealership and orders a 120 point car. The characteristics we look for in a car are multiple and independent: persons seated, trunk size, engine power, speed, mpg, price. No single parameter can summarize them all.
Yet IQ supporters maintain that a single parameter can summarize all mental power of a person. If it were so, then a IQ 120 person would be able to do everything a IQ 110 person can do, with capacity to spare.
As a Gedankenexperiment, take for example two famous Britons of the past: Shakespeare and Newton, and call IQ(S) and IQ(N) their respective IQs. Then either IQ(S) > IQ(N) or IQ(N) > IQ(S). If IQ(N) > IQ(S), that would mean that Newton could have written Shakespeare's plays? I don't think so. On the other side, IQ(S) > IQ(N), then Shakespeare could have written the Principia, which I find also improbable.
The fact that IQ test are composed of different parts, each used to measure a different facet or skill: short term memory, verbal ability, pattern recognition, arithmetics, etc. The final score is a weighted average of the score of the subparts. With different weights, the same test performance might result in different IQs. If the linguistic part is valued enough, then the Shakespeares will turn out with a greater IQ than the Newtons, if it is valued less enough, then all the Newtons will outperform the Shakespeares.
IQ supporters claim that the score of the different subtest are statistically correlated, so they all measure the same thing. If it were so, why have different subtests ? Actually, the correlation is not very high. To return to the car metaphor, we can see that also the car characteristics are also correlated: large cars on average seat more people, have a larger trunk, a more powerful engine, lower fuel efficiency and a higher price, than small cars. Then again, there are sport cars that are small, but have powerful engine and high price, or minivans with relatively small engines, so the average correlation cannot be used to describe a car.