Why does iron have an abnormally high ionization energy? Along a period the ionization energy should increase because the atomic number is increasing, but there is negligible increase in shielding. However, $\mathrm{IE}_\ce{Mn} &lt; \mathrm{IE}_\ce{Fe} &gt; \mathrm{IE}_\ce{Co} &gt; \mathrm{IE}_\ce{Cu}$, so why does iron have such a high ionization energy?

I've considered that iron has a $\mathrm{4s^2 3d^6}$ configuration that goes to a $\mathrm{4s^1 3d^6}$ configuration upon ionization, while $\ce{Co}$ has a $\mathrm{4s^2 3d^7}$ that goes to $\mathrm{4s^0 3d^8}$ configuration, $\ce{Ni}$ has a $\mathrm{4s^2 3d^8}$ that goes to a $\mathrm{4s^0 3d^9}$ configuration and $\ce{Cu}$ has a $\mathrm{4s^2 3d^9}$ that goes to a $\mathrm{4s^0 3d^{10}}$ configuration (Lang, J. Chem. Ed., 2003).  In the Long paper, the authors explain the increase of IE at iron is due to "electronic structure" and I would like to know exactly what about the electronic structure it is that causes iron to have a high IE than expected based on a general periodic trend.

I was thinking that adding an electron to the $\mathrm{3d}$ orbitals might be energetically favorable enough to lower the ionization energy of $\ce{Ni}$, $\ce{Co}$ and $\ce{Cu}$, so rather than iron having a high ionization energy the surround metals just have a low ionization energy because the ion is stabilized by having another $\mathrm{d}$-electron added? Does that sound reasonable?

Another thing I was thinking was that iron is the first transition metal to have a paired $\mathrm{d}$-electron, could that effect the shielding and increase the ionization energy?
"I mean "abnormal" in that it defines a general trend" makes no sense to me at all. Did you mean "defies"?  Take a look at the chart here: https://en.wikipedia.org/wiki/Ionization_energy.
By my count, for the s-block elements the "trend" always holds.  For the p-block elements, it holds in 5/6ths of the cases. And for the d-block, I can't tell from the chart, but claiming it is increasing for them seems agross exaggeration to me; I'd say they might have a very slight tendency to increase, but they're so close to being flat-lined, that it seems to be not a useful claim. If you count the exceptions to the rule, and you expect your "rules" to hold at least 90% to 95% of the time (this isn't the Social Sciences, after all), then it is a just plain lousy rule. Nothing unusual about that: I think the Periodic Table is best when used to "predict" Atomic Number (they increase moving right and down, without exception), and so untrustworthy with the other periodic trends as to not be something in my "mental toolbox". Use it at your own peril. (The at. no. "trend" was a joke, of course)