Why does Chem3D minimize nitrogen dioxide (radical) so badly?
By the looks of it, Chem3D uses generalised classical force fields to describe the molecular interactions.

Such force fields are optimised to provide a reasonable fit to multiple properties for lots of different molecules. For example, they reproduce reasonable bond lengths not only for $\ce{NO2}$ but also for the various bonds in organic molecules.

They are also constructed to reasonably reproduce solvation properties which depend on the molecule-specific partial charges, which in turn alter bond lengths and angles.

So it is unlikely that you have done anything wrong.

If you require a more accurate model, either apply more accurate force fields (e.g. those fitted specifically to $\ce{}$) or switch to quantum chemistry methods such as DFT.