Should I buy a car that has been in an accident?

The car is $500 below Kelly Blue Book. I took a look at it in person. It's in great condition. He said that just a headlight needed to be replaced and the bumper was fine. It's a 2007 Honda Civic with 80,000 miles. What issues would I have with it?

Absolutely not

Are you pretty good with a wrench in case something happens? Do you have a back-up way to get to-&-from work?

NEVER take the seller's word, especially with a car like that.

If the damage is so cheap and easy to fix, you have to ask why he's selling it at $500 below book value. There's no shortage of excellent used cars and your question makes clear that you lack the experience needed to assess the condition of a used car. So either pay a up to couple of hundred dollars to get a professional inspection backed by an insurance to cover faults they might have missed (such services should always also include checks for outstanding finance/stolen/insurance write-offs) or look elsewhere.

On a car of that age, it's also highly possible that light and minor damage has made it an insurance write-off. If you buy a car like that then the future insurance value is always much less than the book value, many insurers won't quote at all, and others will only offer liability cover.

The damage simply means that in addition to all the other issues and risks inherent in buying any 10 year old car, there could be a load of other expensive and nasty faults hiding away behind what seems like minor damage.

Give that car a wide berth and leave the risk to someone who knows what they're gambling on.

If it was just a fender bender it MIGHT be OK… But the problem is, a lot of places will fail to fully report the extent of the damage in order to avoid the car not being sellable afterwards.

Even then only $500 off still seems pretty high. Replacing the headlight and bumper would have easily been $2000-3000.

No

If It was just an accident the car should be fine. Modern body shops can repair a car and put it back in factory like condition using the modern tools and processes.

But be careful. If the car had a very serious wreck or was declared a total losss, salvage, or rebuilt then you don't want anything to do with it.

Repaired or not?

It's the hidden problems you have to worry about, not the ones that are obvious. The dealer may not actually know about the hidden problems since it's unlikely he's done a thorough inspection. He simply want to sell the car as quickly as possible.

Not until it has been fixed. If it is just a broken headlight, someone could have taken the boots to it and broke the headlight. Drunks do weird things.
The mileage is even low for that year. If the body looks good and you have a mechanic(who has the experienced eye) inspect it for a$100 look to be sure, it is a good buy as the car should last till 250K if not more. Bypass the deal and see how quickly it gets sold.
THAT IS THE CHANCE YOU TAKE.
Maybe he want a p_ssy van. Who knows the real reason why he is selling? Only him.
Right now you are using your eyes to inspect it. I difinitely would pay a mechanic to give it a look over… For other expenses that are on the horizon.(maybe the 500 will cover those expenses in part.) You got to figure with it maybe needing a battery, maybe needing brakes, maybe needing a new muffler, maybe needing tires as all that has been used.
. It is expected wear and tear stuff.

"he said"? People selling cars are known to always be truthful when describing the car.
$500 is not nearly enough to justify the risk.