P0420 is a catalyst efficiency fault, it will not affect the performance of the engine. If you have vehicle emissions testing in your are and the fault reoccurs your car will not pass inspection.
Continue driving the car, eventually you may regain confidence in the vehicle.
This is one of those calls that only you can make.
Does the car still meet your needs? Or, assuming you get everything fixed, do you still want (need) the car?
If it were mine… I’d get a new catalytic converter installed at a muffler shop (usually much cheaper) and a new motor mount. All of the other issues can just be “monitored”, and it doesn’t make any sense to get them fixed at this stage of the car’s life.
But I’d stop there. Anything else expensive comes up, dump the car.
you have the term misfire wrong.
the orange check engine light or CEL will flash slowly if you have a misfire. not like a machine gun. slowly
flash slowly, like 1-2 sec between illuminations. sort of a blink on and blink off
you say you “feel” a misfire. what you are feeling is a vibration/shudder from motor that you think is not normal. you wont feel 1 misfire.
if your CEL light is on steady, that means you have a code. yes the light can be constantly on and when you drive you might see the light start to blink on/off. THAT is the misfire “indication”.
Thank you for the clarification. My CEL did not flash. Why did the motor vibrate or shudder?
I called the mechanic again to ask some clarifying questions about why he did not suggest I change my engine mount and it sounds like there varying degrees of “broken”? He said technically it’s broken because the rubber has worn off but it shouldn’t fall through my car like I was afraid of. He said it would get louder and rattle and that’s when I should stop driving it. It does feel a little rocky right now so I should only expect it to get worse. But for an old car like this, I really don’t want to throw anymore money at it. And as for the Catalytic Converter, he said it shouldn’t make my car stop out of nowhere… I would be able to tell when to stop driving it by loss of power and whatnot… so I should be good to go driving this thing casually for the next year or so. Thanks for the responses everybody. Glad I got a second opinion.
Toyota’s of that era had a very tight tolerance for cat efficiency and the P0320 code was pretty common, and very difficult to get rid of.
Most of the time, the actual cause was an exhaust leak before the cat. You had the flex pipe replaced and it is possible that one end of the pipe or the other did get sealed properly.
The next most common source was the rear O2 sensor followed by the front O2 sensor. In some cases where the car sat for too long, the light would go out on its own just from regular driving.
This car has a timing chain and timing chains are lubricated by a fine oil mist from the oil pump. When the engine sits around for a length of time, the chain can get some rust on it and can get some links that no longer want to bend. Either they will loosen up or they will eventually break.
If you have an actual misfire, you will get a P0300- P0304 code. You can get a misfire code from improper fuel mix that won’t set a code and that could be from a gummed up injector. Once you run gas through it regularly, especially top tier gas, it should clean up. Old gas can also cause issues. That does not mean you need a new fuel filter.
The rubber in the motor mounts will develop surface cracks called checking. That does not mean the mount needs to be replaced. I’d just get a second opinion on that because I can’t see your motor mount from here. I don’t think any of the rest of us can either.
As far as the loose hose, that supplies air to the motor to make up for air removed by the pcv valve. If it comes loose, it draws in unmetered air, that is air that didn’t get measured by the mass airflow sensor (MAF) which is located just forward of the filter box. It will cause the air/fuel mix to be so far off that it can cause the cat code you saw. I would replace that hose if it won’t stay on. It could still be leaking with a new clamp on it although I don’t think a good hose even needs a clamp.
I was just WAITING for somebody to essentially say that cats NEVER go bad . . . that it’s ALWAYS the oxygen sensor or an exhaust leak
If you are burning oil that may cause the cat to clog. If the cat is really clogged you can usually see that thru a vacuum test in the intake
I’ll never say that cats don’t go bad…but I guarantee that there have been THOUSANDs and THOUSANDS of cats replaced needlessly.
If you change the word cat to pcm . . . I would agree with you
Otherwise, no dice
Really? Go to Midas or Pep-Boys (pick your national chain) with a code indicating a bad cat or O2 sensor. No further testing…just replace Cat and O2 sensor. Sorry but it’s happened. Midas and Pep-Boys have been sued and lost in court because of this practice.
I’ve never had to replace a catalytic converter on any vehicle we’ve owned…even when they had well over 300k miles.
I reached out to you . . .
I said if you replaced the word cat with pcm, then I would agree with you
I tried to find something we could agree on
I guess it’s no dice
I did try
I don’t disagree that PCM’s are replaced needlessly. But are you saying that Cat’s are NEVER replaced needlessly? If so…then we don’t agree.
I’m not saying cats are never needlessly replaced
But I will NEVER agree that the majority of cats were needlessly replaced
Let’s just end this right now
I never said they were. Please sh ow me where you think I said that. I said there were thousand that were replace needlessly.
Again . . . please let’s just end this right now 
I wouldn’t say majority, but the early 2000’s, Toyota had more than their fair share of cats replaced unnecessarily. The tolerances in the programming for cat efficiency was too tight. Many times after about $3k for a new cat and both sensors, the code still appeared and the PCM had to be re-flashed to solve the problem.
Some states would not allow a vehicle to be re-flashed, even if it was done by a dealer with a factory program so there were some very unhappy Toyota owners. It seemed to affect the Corolla’s the worse.
That’s very interesting 
But I’m done with this particular conversation, as I stated earlier
I’ll see you in an upcoming conversation 