That's a horrible install. There is no way the box on the side of your house should be loose. And cable buried 4 inches, and visible through the grass in some spots, that is just a bad joke. Every reputable contractor that buries things, whether it be phone lines or cable lines, or sprinkler pipes, uses a Ditch Witch and they dig down to a depth of right around 10 inches at least. Perhaps a little deeper depending on how the contractor has it set. But ten inches is the minimum it should be buried.
You should call your cable company up and get a supervisor on the phone. Glorify the situation a little bit to get prompt action, tell him/her that you almost cut the cable with your mower in the area where the cable is visible through the grass. You definitely got a sub, sub standard installation and you should demand to have it fixed immediately.