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The main effects I've noticed when comparing compressed nitrogen to compressed atmospheric air is that when installed in a new tire, the tire with compressed air will lose about 10psi (when initial pressure is 60psi) over the next 6-8 months as the oxygen in the air oxidizes the interior rubber of the tire and is removed from the gas mixture inside the tire. This oxidation caused pressure drop diminishes with time and is negligible in a 5 year old tire.
The other main difference is in the humidity (dewpoint) of the gas in the tire. Compressed nitrogen is generated by boiling liquid nitrogen and so has zero water content. Most garage air compressors just compress the local atmospheric air and don't have an air dryer inline to remove the excess water. Atmospheric humidity rises as the pressure increases, so the 40% relative humidity in the garage's air is over 100% by the time the air compressor has bumped the pressure up to 140psi and put it in the storage air tank (they have to drain the accumulated water from the storage tank from time to time). This humidity drops some when you fill your tire from the storage tank, but the humidity of the air in the tire is still well over that of the initial garage atmospheric air. You can sometimes see this humidity in the air when changing tire as the garage pulls the valve stem and the air rushes out of your tire. This increased water content in the compressed air in the tire is just another gas in the mixture and will react like any other gas to temperature changes. Any corrosion it might do to any exposed steel on the inside of the wheel would end once all of the oxygen in the tire has reacted with the rubber and exposed steel.
I don't see how nitrogen could show much difference in pressure fluctuation with temperature changes when compared to atmospheric gas. All gases follow Charles's gas law and any deviations of nitrogen from that of an ideal gas would be minor.
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