There are certain mechanical issues you may be having with your car that should be addressed quickly but which don't necessarily mean you shouldn't drive your car, at least to a nearby repair shop. That having been said, there are also some mechanical issues that warrant a visit from a mobile car service that will repair the problem on the spot, rather than driving your car even a short distance. If you're not sure if something that is wrong with your car is serious enough to warrant such service, note when it's good to keep your car parked and have a mechanic come to you rather than the other way around.
1. When brakes stick after releasing the pedal
There are a few reasons why brakes might stick after releasing the pedal, and all of them can signal a serious problem with the braking system that might allow the brakes to fail when on the road. If you notice a grinding noise and severe drag with this problem, the pads may have slipped out of place. If they should slip completely, they can wedge themselves in between the tire and the rotor and the car can slam to a stop. Smoke coming from the tires after you release the brake pedal often means the same problem.
In some cases, the problem may be that the brake pedal itself is stuck; the lever that releases the pedal when there is no weight on it may be corroded. If you drive your car this way, the pedal may get stuck altogether and your brakes don't release at all. Your car's computer may also be acting up; if it cannot sense that you've released the brake pedal, it may continue to apply the brakes and, again, they may simply seize up while on the road.
2. When tires are shredded
Tires don't need to be actually in pieces to be considered shredded; if there are metal threads that jut out from the tire's tread, you don't want to drive your car this way. These metal threads are part of what give the tire's rubber its strength and when they're exposed, this means the rubber has been worn down to its inner layers. It can then be at risk of blowing out when on the road; flying rubber can cause damage to other cars and a blowout can make your car skid and slide when you least expect it. For your own safety, have a mobile car service put on a spare tire or replace the tire before you drive the car.