Why oxygen leaks from tires faster than nitrogen? In critical applications tires are inflated using pure nitrogen (link).


  Nitrogen molecules have a more difficult time escaping through the
  microscopic spaces that exist between a tire's rubber molecules. [...]
  Nitrogen reduces the loss of tire pressure due to permeation through
  rubber over time by about 1/3. (source)


According to WebElements, nitrogen bond length (109.76 pm) is smaller than oxygen bond length (120.74 pm), so why nitrogen permeation through rubber is said to be lower than oxygen?
The rate of oxygen, $\ce{O2}$, permeation through tire rubbers is about 3.4 times faster than nitrogen.  The reference for this is "Permeability Properties of Plastics and Elastomers" by L. W. McKeen.

The reason is that $\ce{O2}$ is a smaller molecule than $\ce{N2}$.  The size of a molecule is not determined by only the bond lengths between atoms but the size of the electron cloud around the atoms.  The kinetic diameter of $\ce{O2}$ is 0.346 nanometers and $\ce{N2}$ is 0.364 nanometers.  So, $\ce{N2}$ is larger than $\ce{O2}$ even though the $\ce{N-N}$ bond length is shorter than the $\ce{O-O}$ bond length.