Somewhere here it was suggested to include a needle nose plyer in the repair kit. Together with the tire plug and cement, and tire plug insertion tool(s), practice (use an old tire to learn how to place the plug), combined with the compressor and slime (read the directions and decide if it's for you...) you can deal with some problems and get off the road.
Sidewall cuts are usually fatal to the tire. High speed interstates are not the place to take apart a wheel and work on it. If I could not get well off the road without getting stuck, or had a sidewall disaster, I probably would phone AAA and call my next destination reporting my planned lateness...
Read your owners manual while you're waiting for AAA (you will have plenty of time), locate the tool you need for removing the front panel below the chin (what? There's a tool for that?!) and if the driver goes for the front, do him the courtesy of removing the panel and showing him the proper anchor point. Your front suspension will thank you...
And I'd watch the AAA flatbed operator like a hawk to make sure he doesn't blindly fish around under the car until finding "something solid" to put his meat-hook and chain onto. I hate to say it but a large number of these guys are know-it-alls and don't like being "coached". But being a know-it-all myself, that makes us even and since it's my car and me paying, I get to be in charge... As my wife likes to remind me "Say it like you mean it but you don't have to be mean when you say it..." Yeah OK.

Does it count that I always tip the ones that do what I tell them and send the ones that don't away without me?
Or if you really think all this sucks, go get a car with a full sized spare and learn to use the jack.
Now having said all that I am hoping I have counterbalanced the bad juju I am about to create by saying "I have not had a flat and I'm on my third set of tires for this car." Oh no! Seriously, one thing you can do for yourself is stay out of those little piles of sand and crap that pile up on the side of the road and in between the on-ramp and the main lanes, and pay attention in gas stations and parking lots - there's lotsa crap you don't want to drive on that gravitates to the sides of the lanes and never mind how it gets into the driveway of the gas station....
Today I came around the corner in the parking lot at work and there was a perfect piece of slate shaped like a triangle standing point up, about three inches tall with a nice indian arrow head edge. Just another rock on the road if you're not paying attention. Yeah, I skipped that roll of the dice.