When you have nitrogen in your tires, should you maintain the same tire pressure as is recommended by the vehicle manufacturer or should you increase the tire pressure? 
May I piggy back? If you have nitrogen in your tires because you got upsold, but then you had to replace a tire and they replaced it with no nitrogen, do you have to get that tire nitrogened or is it okay to have three of one and one of the other?
Air is already 78% nitrogen
Yeah, I got upsold.
Whether the tire is filled with air or filled with nitrogen has no bearing on the pressure, nor is it a concern which of those the tire may have been filled with previously, nor which of those is in the other tires. In sum, for almost any question about using air vs. nitrogen for ordinary passenger vehicles in ordinary circumstances, it doesn’t make any significant difference.
Gas pressure is gas pressure. Your tire neither knows nor cares what the gas is. Use the same total pressure no matter what the gas is.
pV = nRT
The ideal gas law really doesn’t care what the gas is (as long as it behaves approximately ideally), so nitrogen, air, sulphur hexafluoride, oxygen, carbon dioxide, argon would all behave exactly the same in your tyres. The only difference is purely chemical - the way the gasses react with things they come into contact with. In terms of the physical performance of a car-sized tyre, the gas is really not a concern.
You could probably even fill your tyres with Radon if you could find a source and were willing to pay the very high price. Make sure you finish your trip in under 4 days though, since half of your radon will have decayed into lead.
(disclaimer, please don’t fill your tyres with Radon, it’s radioactive and expensive).
IMO all good things are those two things.
Its my understanding is this nitrogen thing is that there is no oxygen in there. In theory, no oxygen means no oxidation of the rubber inside the tire. In practice it probably doesnt make a hill of beans difference. The fact that if you use tanked nitrogen, the stuff probably doesn’t have much water in it, which is probably a bigger advantage (though still minor) than the lack of oxygen in it.
SD column for reference: Is it better to fill your tires with nitrogen instead of air?.
We had a similar thread earlier here http://boards.straightdope.com/sdmb/showthread.php?t=558323
Pretty much I’ve come to the conclusion Cecil blew it when it comes to pressure loss in a N2 vs. air filled tire.