Q: what other issues can occur if a misfire troubleshooting problem is not fixed soon enough?

Unfortunately, it is possible to damage the catalytic converter, that is cause a blockage, if the engine misfires "too much" and/or for a prolonged period. It is not yet known whether your converter is damaged, but I will get to that. What happens in a misfire is the fuel doesn’t get burned in the engine cylinder. The fuel, though, has to go somewhere, and the "somewhere" is out the exhaust past the catalytic converter. But, a catalytic converter is NOT intended to be a combustion chamber and unfortunately when the unburned fuel from the engine reaches the converter, it "lights off" in the converter, that is burns, raising the internal temperature high enough to melt the internals of the converter thence blocking the normal flow of exhaust gas. If the converter gets blocked due to this damage, which again could be caused by misfiring, the engine won’t work very well. If the converter is blocked, for you to figure this out, all you need to do is ask the mechanic if he or she evaluated the upstream VERSUS downstream oxygen sensor readings. If the upstream sensor has a normal waveform and the downstream holds STEADY at about 0.5 volts, your converter is "probably" functioning. Additionally, ask the mechanic what the measured temperature differential is at the converter inlet, versus the outlet. The outlet temperature should read as much as 100 degrees F HIGHER than the inlet temperature. If there is no difference, the converter is not functioning. Finally, ask the mechanic what the exhaust back pressure reads ahead of the converter. It should be really, really low. If not really low, the converter or, a component after the converter, is blocked.

As far as the oxygen sensors, mass airflow sensor and anything else you are being told is defective, ask to see specific test results on a scope or diagnostic tool. For whatever reason if such are not available, don’t exist, or are never shown to you, run for the exits. Do not replace anything without an INTELLIGIBLE explanation, and the explanation MUST include actual tangible evidence of a fault or defect. As far as where to go from here, due to the misfiring, the claim of the dealer that the converter is faulty, and the symptoms you are reporting, the first thing to do is get the issue with the converter, and any exhaust LEAKS (leaks are dangerous) fully resolved. Once the converter issue is fully resolved, and there are no exhaust leaks, if a remaining issue(s) exists with the engine or the rest of the vehicle, such can be dealt with in turn. If you want a certified mechanic to fully resolve the converter issue, simply request catalytic converter diagnostic/replacement and once an intelligent and complete diagnostic is done, if you actually need a converter and you desire that the mechanic install one, he or she will do it. By all means, if you have further questions or concerns, as you wend your way through this, do not hesitate for a moment to re-contact YourMechanic and we will assist you further.