What effects can having a deep dish wheel fitted to your car have?

If the wheel ends up sticking out past your fenders, the police may pull you over for it.

If the middle of the tire ends up not the exact same distance from the middle of the car as it used to be, you can mess up your handling, and ruin your steering bushings and other front-end parts. Ruining these parts is bad because they are expensive to replace, and it's very dangerous to drive when they need replacing.

Otherwise, you're just wasting money. If it's your money to waste, you're good; just don't borrow money for wheels.