1. Strong radio transmissions (eg, from adjacent / nearby Police car, Ambulance or mobile
Amateur Radio station(s), some of which can emit ~100 watts of RF power, if necessary to maintain comms with others in their nets) can affect some cars' microprocessors.
To the best of my knowledge, this sort of interference should be quite unlikely to occur. The car's computers are contained in grounded metal enclosures, so any induced interference should be grounded away from the computers. Additionally, digital devices, unless they operate at a very low voltage (probably less than 500 mV) are not extraordinarily susceptible to electronic interference. That said, very unlikely doesn't equal impossible.
2. I've seen warning / disclaimers on CPU & MPU documentation, to the effect that their manufacturers do NOT warrant their products for any systems / applications (eg, pacemakers or, I would suppose, automobile / engine control, etc.), that could cause death or injury to humans.
Perhaps, despite the best intentions of the makers of MPU's used in Toyota's vehicles, some will "just get stuck" and (I presume) need to be reset by a watch-dog timer / circuit.
This kind of thing happens all too often in the PC world, and could possibly happen (if less often) in auto. / engine systems.
In a typical car (disclaimer: I don't know whether Toyota builds theirs this way) the engine control unit will control many engine parameters beside the throttle; fuel injection, fuel-air ratio, RPMs, etc. If the ECU were to crash, the engine would just stall (not that this couldn't happen, of course; however, "My car stalled, but it started again a minute later. I took it to my mechanic, and he couldn't find anything wrong." doesn't make for high-visibility recalls.)
For the unintended acceleration problem to have an electronic or software-related cause, several largely independent systems in the car would have to fail in fairly specific ways at once, which is a one-in-a-million occurrence. Of course, there are how many millions of Toyotas on the road?
I tend to think that Toyota's mistake in all of this initially was to work backward from the assumption that every instance of unintended acceleration has an identical cause. It's also pretty obvious that they initially had no idea of a possible cause. Compounding this is that the condition is quite rare (there are, what, a few dozen confirmed reports?) We know that there are at least two causes already: Floor mat interference with the accelerator, and a mechanical flaw in the accelerator assembly. I suspect operator error could be a possibility in some cases, as well.
3. If no other causes prove to solve these mysteries, I would might begin to suspect some form of misguided, rumor-based collusion, on the part of disgruntled individuals (eg, due to the Chapter 11 filing of General Motors, in recent year(s)), or others pursuaded by reports
I think this is a bit paranoid. I don't think Toyota has had significantly more complaints of unintended acceleration than any other manufacturer, once you adjust for market share, but the raw number is much higher, so they are subjected to increased scrutiny. If it is some sort of conspiracy, I don't think it will work out all that well, though; I read that the overwhelming majority of Toyota owners would still purchase another one in the future. Toyota does have a lot of brand loyalty and good will, though they are undoubtedly spending some of that now.