These are a few of the many, many parades happening. The key thing to remember is that when the parades are running, all traffic stops. The cops do not care about your problems, this road is closed. If you car is towed, you can find it at 400 N. Claiborne, sorry no out of town checks accepted. Also watch for the posting of temporary signs along parade routes.
Security is good during the day and most day parades are safe even downtown.
Be very cautious of the parades downtown at night, and in particular be careful parking in out of the way places. It is usually safer to park up in the garden district or near Tulane and take the trolley downtown if you are going to the quarter or to see a parade along Canal. There is for all practical purposes, no parking around the quarter during Mardi Gras at night. In fact you need a pass even to drive into the Quarter. They take MasterCard, Visa, or Traveller Checks.