Other mistake: When Slim is getting ready for the fight, she gets out a device to interrupt cell phone service. When she gets out her cell phone to test it, her phone reads something like 'No service', yet it shows that it has all five bars next to the antenna.
Other mistake: When Noah Wyle runs up to Jennifer Lopez's car, he's trying to open the car door, but it's locked. Yet, at the top corner of the screen, in the view from inside the car, there is a thumb sticking inside the car.
Other mistake: When Jennifer Lopez and her daughter are driving in the old Ford Crown Victoria and discussing why they are running away, there are two shots of the speedometer. The speedometer clearly reads between 15 and 20 mph. They are driving on a highway, and the scenery outside the car is going by at a much faster speed.
Other mistake: In the final confrontation, Slim explains her plan how to make the beating look like self-defence. She tells Mitch her plan is going to work because he touched her letters she put into his drawers. All right, Mitch did touch the letters when he wanted to retrieve his gun. But from where she was standing, Slim could not have seen that he really touched them.
Answer: I wonder if the nickname is related to the difficult times in her life. Her father was not around. She and her mother did not have much money. Maybe she felt that she had a "slim chance" of life getting easier.