Can nitrogen dioxide react with plastics of any kind?
Nitrogen dioxide is a free radical but its energy is rather low so it will be unlikely to be able to abstract a hydrogen from most polymers. If we consider polypropylene as the "standard plastic" then I would not expect nitrogen dioxide to be able to corrode it by abstracting hydrogens from the plastic.

But if we choose something else such as an epoxy as the standard plastic then nitrogen dioxide when combined with water could start to chemically alter the plastic. It can react with amines to form things such as N-nitroso compounds.

When nitrogen dioxide dissolves in water it forms nitric and nitrous acids. It can be regarded as a mixed acid anhydride for these two nitrogen oxy acids. The nitric acid could also start to degrade and alter plastics such as epoxy plastics by nitration of electron rich rings.

The acid formed when nitrogen dioxide dissolves in water could degrade plastic by increasing the rate at which esters such as the phthalate diesters react with water. It is important to keep in mind that many plastics are a combination of a polymer (or several polymers) and some additives such as plasticisers. If you degrade the plasticisers some plastics will stop being "plastic" and become brittle.