1. nitrogen is very dry (dewpoint of -40F or better).  So, compared to compressed air it is does not change pressure as much with changes in temperature. 

2.  Air is approximately 79% nitrogen and 20% oxygen, with the rest including other gases such as argon and helium. Oxygen is bad for tires, causing degradation of the rubber compounds.  Street tires have been designed to resist the oxidation, but some still occurs. So, some car restorers and others will use nitrogen to extend the life of their tires if they intend to keep them on for a long time or in storage. 

 

Racers will often use nitrogen because it is more stable with temperature changes, compared to air. 

 

For street applications, it really doesn't make sense to go through the expense of nitrogen. I can get mine for free and I don't mess with it.  To use it effectively you need to fill and purge the tire several times to remove air, or use a dual tire valve setup so that you can bleed air out while filling with nitrogen.