Yes, I'm afraid that you do have to be careful about storing a knife in your car for two reasons:
The first is legal. You may think of it as a tool for cutting seatbelts, prying open car doors, whatever, but when a prosecutor trained in courtroom theatrics holds it up in front of a jury, it may look quite different. In many states, a knife kept in your car in such a way that it can not be readily seen by a police officer approaching you but yet is readily accessible by the driver is considered a concealed weapon and is seriously illegal regardless of why you keep it there.
The second is safety. Years ago, I was in a car accident. It was a roll-over situation. The car rolled three times. The forces are quite violent. Every compartment in that car, center console, arm rest, map pocket, glove box, ash tray, every one of them opened and spilled its contents into the passenger compartment. As I went round and round, all of that stuff was flying around with me. I found the Benchmade 970 which had been in the glove box, locked open and stabbed into the back passenger seat. That's right; there had been an open BM970 flying around my head. After this experience, I've adopted one simple rule: if you wouldn't want to get hit in the head with it, put it in the trunk.
Double-sided tape? Velcro(tm)? Suction cups? These things will not withstand the forces of a serious accident. If you want to mount something in your car, then you need to break out a drill and bolt it down.
I have a friend who "installed" a stereo in his car. He attached the speakers to the back deck with Velcro(tm) so that he could remove them easily and cleanly if he sold the car later. They seemed firm enough. And, yes, he did end up selling the car... to his insurance company after he totalled it in a classic rear-end colision. He was going about fifty when he hit the back of the truck stopped in front of him in dense fog. When your car goes from 50MPH to 0MPH instantly, the forces involved are huge. One of the basic rules of physics is that an object in motion tends to remain in motion. Those speakers on the back deck? They were objects in motion at 50MPH. When the rest of the car stopped suddenly, they remained in motion. Those speakers tore off of that back deck and flew forward. The one on the driver's side missed my friend's head by maybe an inch or two. He was lucky.
Many people do like to carry a knife as a weapon. They're afraid of getting carjacked. But I think you'll find that more people are in car accidents every year than are carjacked. The cure for the one problem may easily end up hurting you in another way.
So, do I carry a knife in my car? Of course. It's an 8" fixed-blade Kershaw, in fact. And it's in the trunk. Legally, it's not a concealed weapon because it's not readily accessible to the driver. And because it's in the trunk, it's not going to end up in my chest in an accident.