There are two levels where you can make attempts to maximize your cash flow, in Free Play:
Fast Money - Two Face Chase:
Fast/short level with roughly 100,000 studs. Make sure you have -Harley Quinn's Hammer Truck-. It can run over lots of obstacles that other vehicles can't, and it has a great turning radius.
I like to have the -Batmobile- as the second vehicle, so I can finish each section off quickly, and just run around shooting as much as possible. Once you have stud multipliers, this level gets you some big money rather quickly.
Easy Money - An Enterprising Theft:
At this point, the only useful character you won't have in your arsenal is -The Joker-, but he won't be necessary. The two characters you need are -Sonic Batman- and -Mr. Freeze-.
Get past the first room with the escalators. In the second room, assemble the push button to release all the toxic material. Use -Sonic Batman- to open the glass door containing the lone engineer. Switch to -Mr. Freeze- and use his ice blast on the guy. This will cause him to spill 10 point studs out like a fountain, and he doesn't die.
This can take a long time, but if you get him stuck just right, you can tape down the button on your PSP and just let him go at it.
For best results, have -Stud Magnet- turned on and surround him with another Mr. Freeze.