Nitrous:
To get the nitrous from the used parts shop you have to lose the "Sega Drag Racing" event on a day that ends in "5" like 155, 185, etc. The next day "Nitro" will be available in the used parts shop. After installing it you can use it during a race by pressing Y. Note that you can only buy and use Nitro once. 

Easy Money:
Unlock the GT40 Concept car from the Season 1 Official Races. You can buy it for $150,000 then sell it for $185,000 - $195,000. It takes one or two game days to sell it for a $35,000 to $45,000 profit. 

Free Parts Glitch:
If you have the same amount of money that a part costs, you can usually buy it without losing any money.