Funky ignition - safe to drive?

My 2000 Honda Odyssey has some electrical issues. Always has had them. Nothing that would reduce its functionality and it only happens sometimes. Here are two examples of ignition incidents:

Once I was sitting in the car with the key in the ignition in off position. Somebody opened the passenger door to get in, the car started on its own. I wasn’t able to turn it off by turning the key since it was still in off position. Even turning it to on and then off, wouldn’t shut down the engine. What finally worked? Pushing down on the brake pedal.

Another incident this morning: I accidentally left the heat running with the motor off, so the battery died. I tried to start the car a few times, but nothing. Then I pulled the key out of the ignition and was getting ready to get out of the car, when suddenly the car tried to start on its own without even a key in the ignition. It tried a couple of times. I was able to stop it by locking and unlocking my door.

My question: These incidents are rare and not related to moving traffic. Is it possible that those electrical issues could have an impact on safe driving at some point? E.g. Car shutting off while driving, or starting without parking break in.
Do I need to have it fixed? Since this car is old and we will replace it as soon as costly repairs are needed, I really don’t want to put any money into it.

The problems that you describe are the result of a remote start system that is acting flukey.
Is this a safety hazard?
In my opinion, it is–or it will be very soon.

I suggest that you have a mechanic disconnect the remote start system, as that should–hopefully–eliminate the problems.

What’s that?
You say that it doesn’t have a remote start system?
Unfortunately, you are wrong.
Most likely, the previous owner installed it, but did not inform you of its presence.

;-))

The electrical systems can get funky. We have after mafket 2 way radios, and in a Sienna van the guy wanted a power point, so I tapped off the feeds for the 2 way radio to power a spot light. If he left the spot light plugged in the key would not turn off the engine, but the engine if the key was off would turn off when one opened the driver door. Had to change the wiring but my point is any after market stuff has the potential for doing something un expected.

@Lincnic check this out. Even though the symptoms don’t really match yours, maybe you’re still eligible for that free ignition switch.

http://109.87.33.216/manuals/auto/Honda/83.pdf

If the starter motor engages and stays on, it could overheat and create an engine fire. Unless you disconnect the battery each time, I wouldn’t park this car inside a garage until this remote start problem is fixed, for fear of setting the garage and possibly the house on fire. Keep the car parked outside on the street. I had a friend who’s car caught on fire because the starter motor got stuck in the on position. She had to call the fire deparment, and the car was completely burned up and 2 other cars parked nearby were damaged. Fortuneatly, the car was parked in the street at the time.

Fire is a risk. So is carbon monoxide poisoning. I’d get it fixed.