I'm quite a fan of keeping redundant kits just about anywhere I spend a lot of time--including car, home, and work. My car kit is pretty extensive, and I won't go into all of the contents, just for time's sake, but a few special considerations I'll pass along, for whatever they're worth.
1. I live in Arizona. This means that there are days when the air temperature outside is going to be 115 degrees Fahrenheit, plus, every year. That's air temperature, in the shade, measured about 6 feet off the desert floor. Temperatures inside a car can easily exceed 150 degrees. In the winter, it'll freeze. In short, I know that whatever I keep in my car has to withstand great temperature variations. Thus, I avoid candles (they'd melt); I'm careful with what leather I keep there (at least treating it heavily with mink oil or the like, to keep it from literally crumbling to powder), that kind of thing.
2. Cars are easily broken-into, and many of them have very limited space in which you can hide something. So, one thing I try to avoid is keeping my survival stuff in one visible bag or backpack. Either I keep a packed pack in the trunk and out of sight, or I scatter the survival gear item by item around the inside, on the theory that while a bulging backpack might look valuable to a thief, a roll of paracord, some packages of ramen noodles, etc., etc. may not. Probably good to keep a day-pack stowed somewhere like under the spare tire or under a seat so that you can load the stuff in and hoof it if your car's disabled, but making it unattractive to thieves is good. Also, I rarely keep valuable stuff in the car. My wife is often distracted and forgets to lock the doors, and I figure I'd rather leave a Cold Steel Trail Hawk and a $10.00 Mora knife vulnerable to theft than something I'd really miss were it stolen.
3. One advantage of a car is that weight can be less of an issue than with on-your-person kits.
4. Remember that it's a car. Part of survival there is making sure the car will keep going. Things like a jumper cable may not sound like exciting "survival gear", but you're likelier to need that than, say, a machete. Remember that a flashlight can be handy for figuring out which battery terminal is which.
5. I'm often VERY happy that I've got basics of everyday life stowed in my car. Yes, I can build a brush shelter with the best of them--but if you're equipping your car, why not toss in a 2-person tent next time they go on sale for $24.87 at Wal-Mart? Unlike your brush shelter, that'll keep out the ants and mosquitos. Likewise, food: I know what's edible, plant-wise, in my area--but why force myself to rely on that when I can toss a box of granola bars and a Wal-Mart box of ramen noodles in the car? The noodles have the advantage of being edible without necessarily having to cook them--something less true of, say, beans and rice. Cheap is good, too--and I notice that I can buy a small case of ramen noodles for less than I'd pay for 3 MREs. Oh, also, think about the others who'll likely be around--wife, kids, other drivers stuck in the evacuation traffic jam; it's always good to leave yourself options besides "I have just enough food/water/shelter for myself; sucks to be you." Once I had the clever idea of putting one cold-weather cap in the car for each member of my family--and when the weather turned unexpectedly cold at one of my kids' birthday parties, I broke out the caps and loaned them out--but discovered that it's nicer to have a few extra, since there are often others you'll want to take care of, too. I now have maybe a dozen cheap, red or orange cold weather caps in a bag under one of the seats of the van, because they're a cheap, readily-stored, doesn't-hurt-much-if-someone-walks-off-with-it way of maintaining basic bodily warmth. I've got a lot of kids, so a couple of spare diapers are a very wise investment. I also often keep a little low-volume, low-weight items like tea-bags and powdered cocoa, just based on the experience that a little hot tea or cocoa can help the morale of the people you find yourself surviving with.
6. Water is a must. Don't count on finding and purifying it--just carry some. Carry a lot. It's not bad to see to it that whatever vessel it's in is something you can carry, if need be.
7. Like most of my survival kits, my car kit items tend to get used most for unexpected non-emergency things. The multi-tool blade may not have cut much tinder or freed people from many seatbelts, but it's sliced a lot of apples for the hungry kids in the back seat. The compass I keep within the driver's reach I use for simple car navigation, though I originally contemplated using it in an SHTF hike-back-after-car-dies situation.
8. One more consideration about a car kit: anything in your passenger compartment that's not secured may become airborne if you crash, roll, go airborne, or it gets shot back by a deploying airbag. One of my EMT instructors regaled us about an accident victim he saw who ended up with a gearshift lever up his--well, let's say an awkward and uncomfortable place--after rebounding off the passenger-side door during an accident. It's a good idea to make sure that anything heavy or hard isn't going to become a bullet if your car goes down an embankment. This point was brought home to me after my brother survived a rollover in the Arizona high country. The Land Cruiser he was in hit some black ice on a curve on the road, flew off the road, went completely airborne for maybe 20-40 feet, snapped a pine tree into 3 pieces, landed in the snow, and rolled, coming to rest on its side. All the guys in the vehicle were unharmed, except for a scratch here and a bruise there. Reason: all were in their seatbelts, and nobody got hit by any of the heavy gear that was in the passenger compartment.
9. It's a great idea to keep a master list, in pencil, of the gear you've got, and where it is. That way, you can find it if you forget, and your wife, kid, etc. can also figure out where you hid it if for some reason you're not available when the survival gear becomes needed.
10. If you have anyone you're interested in rendezvousing with (e.g., your wife and kids, if you spend most days at work like most of us do), have a clearly-established meeting point, preferably scouted out on a trip in advance. Not a bad idea to have some kind of arranged way to leave a message, in case one of you gets there first, then has to leave--it may be really great to have an arrangement like "if you get there, but then go somewhere else, leave time you were there and where you went on a piece of paper duct-taped to the back of the stop sign"
