Any recommendation depends on your location - I wouldn't provide the same answer for Yuma, AZ as I might for Edmonton, AB.
When water vapor diffuses through a wall and reaches the exterior sheathing, if that sheathing temperature is below the dew point the vapor will condense. Depending on the amount of water vapor and the rate at which the wall cavity is able to dry out, this may lead to moisture problems.
Installing insulation in the wall cavity will help reduce heating costs, but won't address the problem of sheathing temperature. As a result, some builders are specifying 2" to 4" or more foil faced polyiso panels be installed outside of the sheathing to raise the temperature above the dew point. In these designs, some don't even advocate using cavity insulation. Vapor will still diffuse into the cavity, but it will not condense on the sheathing surface.
Installing foil faced polyiso on the interior of the wall, properly air sealed and with taped joints, forms an effective vapor barrier which will reduce the problem of moisture diffusing through the walls. However it may not solve all of the problems with vapor diffusion so it's quite possible to still have problems.
Additionally, while most people look to insulation as a primary solution for energy savings, often older homes would find greater benefit from air sealing. There is almost no way you can make an older house with plaster walls "too tight." In fact, the idea of houses being "too tight" is something of a myth. Your goal should be to have "managed ventilation" rather than the unmanaged ventilation common in older homes.
In my 1870's New England house as an "inside" solution I removed the plaster, installed fiberglass batt insulation in the cavities, applied 2" foil faced polyiso over the studs (for a thermal break and vapor barrier), with 1x3 furring strips and gypsum on top.
You had (maybe sub-optimal) working air, so the holes (unless new) are probably not the primary cause. I imagine your evaporator coil (the coil inside the interior air handling unit) has frozen over.
This typically happens when the airflow over it is restricted, but it can happen when the refrigerant has leaked out of the system. Air restriction prevents warm air from heating the coil, which will eventually freeze the humidity out of the air creating an insulating block of ice. Low refrigerant levels super cool the coil creating the same freezing over.
So, replace (or temporarily remove) the dirty air filter. Open all the vents. Turn your AC off for a long enough period of time to melt the ice (typically 4 to 5 hours, but sometimes less). Then turn the unit on. If airflow is restored, you know the symptom of your problem.
If you don't freeze up again, it was likely an airflow problem you just fixed with the new air filter and by opening the vents. Occasionally the interior fan is not turning on, so opening the interior unit is a good idea for visual inspection.
If air handling seems fine and it freezes up again, call a professional to find the leak in your system, have the leak repaired and then get your system recharged with refrigerant. Many pros like to charge the system and run; but, refrigerant doesn't degrade or get "used up". If you're low, there's a leak. Get them to find and fix it now or risk calls and extra strain on your system (which could shorten the life of your system).
Opening the unit involves removing the tape around the panel (it is typically metal duct work tape, so use gloves to avoid cutting your hands). The tape only seals the unit for air tightness. There are screws on the panel. When done, re-tape with metal tape for air tightness.
Keep in mind that the root cause is sometimes electrical. If so, you'll notice the interior fan not is not turning on. There are additional circuit breakers on the air handling unit, as well as the possibility of burnt out control circuitry, corroded / disconnected wiring, etc. It is a good idea to turn the breakers off and on just to assure it's not the cause.
I'd fix the duct work, but to save you money on your AC bill, it's not a likely root cause.
Best Answer
If the evaporator has to come out, you'll likely have to recover the refrigerant first. Unless you have the proper equipment, you're not going to be able to do it yourself. Even if you have the equipment, you may also need to be certified to complete the work.
If you can replace the insulation without removing/damaging the refrigerant lines, then you might be able to do it yourself.