I just beat the game and I noticed a few things that are oddly legal. I'd like to compile a list of things you can do without ever making Liberty city's finest mad. Here are my rules. 1. You must assume cops see you at all times. 2. You can't get a wanted level of one. 3. It can't be part of a mission or other one time event. 4. It doesn't have to be profitable to be added to the list but profit means an automatic add. 5. No cheats.
Here's the things I found so far;
Running into people (walking not punching) can hurt them, but cops don't mind. Push them down over and over and slowly kill them and take the cash. It's a bit tricky, but you can also push them into the road.
Crashing into cars at high speeds sometimes kills the driver. If they fall out you win a prize.
Running into a securicar over and over until you can blows up on it will destroy the both cars winning you a large prize. However this requires a car and they are hard to get without breaking the law.
One way I found to get cars is by calling cops, fire department and paramedics to your hide out. If you get them to stop on your parking space you can sleep in your bed and the car will be yours. However this doesn't always work right. Sometimes the car isn't your even after it's saved to your space.
Getting people mad at you by pushing them down and then getting them to fight cops by standing near can sometimes win you some ammo.
Aiming a gun at people won't bother cops unless they are in the middle of you and the person. They normally just run around like crazy so it's good for anything fun it's funny.
That's all I can think of at the moment, but I'll add more as I think of them and find them.