Why does iron consume more energy in the fusion process than it produces? I understand that once a star starts fusing iron, it's doomed to collapse because iron fusion requires more energy than it releases in the process, allowing the opposing gravity of the star to cause it to collapse.

But why?  What makes iron special in this way?  It seems to occupy a pretty inconsequential spot in the middle of the period table among the transition metals.  So, why is it that iron breaks the rule in play for all the elements before it when it comes to fusion?

I noticed that on another question someone said that it wasn't iron, but nickel that was the first element that required more energy to fuse than it released- but every documentary and book I've read claims that it's iron.  So, if you're answer is "iron isn't the first element that requires more energy..." please explain why every other source I've ever heard is wrong!
It would be good if you referenced your sources, because you may be misunderstanding them. We'd be able to see what they actually say, and help you understand them.

Nucleosynthesis of iron does not use more energy than it produces.

It is, however often referred to as the heaviest element created in fusion that results in more energy produced than consumed.

However, that isn't quite true. Heavier elements can be produced by fusion that produce more energy than is used, except these fusion reactions don't occur in stars. (Eg 40Ca + 40Ca)

Also, it is possible for heavier nuclei to be fused in stars that result in more energy being produced than is used, but these are unstable isotopes and they decay quickly. 

So, more accurately, iron is the heaviest element produced in stellar nucleosynthesis in any significant quantity that produces more energy in fusion than the fusion consumes.

This is called the alpha process ladder. Keep adding alpha particles to the newly generated nuclei, until you stop getting more energy out than you put in. 

The last step in the alpha process that does produce energy is 52Fe + 4He => 56Ni(excuse the rubbish notation; if this answer is considered helpful at all I will try to tidy up the notation)

56Ni + 4He => 60Zn uses more energy than it produces. 

56Ni has a very short half-life of just 6 days, decaying to 56Co which has a half life of 77 days, which decays to 56Fe, which is stable. So when a star is on the limit of collapsing, it will be producing a lot of iron in it's final stages - some of it from decaying heavier radioactive isotopes.

Why does the alpha process stop producing energy at this point? It is because that is where the peak binding energy is. More.