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.
Fixed! Turned out, it was an issue with the condensate drain line.
I had moved it and it had become just ever so slightly raised, so that the line had become double trapped. The collector was filling up with water, and tripping the secondary pressure switch.
The reason I wasn't getting a code, was because the water was gurgling, or bubbling, as the negative pressure pulled the water back up the condensate line. This caused the pressure switch to fluctuate rapidly, which is also what caused the sputtering flame problem. This rapid fluctuation, which was picked up by a multimeter, was too fast for the control board to actually register a fault.
Fixed the condensate line, and all is well.
Haven't been able to explain the cover on/cover off phenomenon, may have simply been coincidence. It ran all night, all buttoned up, without issue.
Best Answer
Start collars and take offs are terminology that are used interchangeably. Finger type ( fold over tabs) are generally used in duct board plenum and trunk lines. Collar types are used with sheet metal distribution systems. Sheet metal uses three short metal screws in each collar with mastic or other sealing products. The finger type collar has flexible duct attached with a first layer duct tape, attaching the inner liner to the collar. Next is a coating of mastic over the tape completely. Pull the flexible insulation and vapor barrier over the joint and secure with a large nylon zip tie. Trim the zip tie and you are done.