The problem you describe is considered normal performance for many residential A/C units. By design, these only function correctly if the outdoor temperature is warmer than mid 70s and the indoor temperature is above 68F. Below these temperatures, the evaporator coil gets colder than freezing, becoming worse as the coil accumulates frost, eventually causing the system to become covered in ice and stop cooling until the unit is manually shut down and thawed.
In a situation such as yours where A/C needs to perform even during cool temperatures, it is necessary to install three accessories which will enable the unit to operate under these conditions:
(1) A compressor crankcase heater (sized for your compressor)
(2) A head pressure control (such as Totaline p251-0083h, approx $35 new, Ebay)
(3) A evaporator control limit (ECL) switch or Freezestat (approx $20 new, Ebay)
Calibrating the head pressure control perfectly requires a set of gauges, but it usually works correctly if the temperature probe is placed anywhere near the discharge of the condenser coil. Other than that, these are electrical items only, requiring no refrigerant expertise. This setup is sometimes referred to as a "low ambient kit with freezestat." An experienced tech should be able to install all these within a couple hours.
the air filter is designed to clean the air flow prior to passing through the fan or the heat exchanger. its a common misconception that the air filter cleans the air for us humans. its there to keep the air clean for the machinery. its a secondary benefit that the air is cleaner for us. if you get a buildup of dust inside the fan, you get overheating of the motor, inefficient air flow across the vanes, even fires from localized buildups. if you get dust buildup in the heat exhanger, it can massively shorten the life of the furnace (particularly in electric furnaces) or cause an outright fire.
if you cant get a cartridge filter to fit your furnace, get an hvac company to come in and install one between the cold air plenum and the furnace intake. then you can keep the furnace cleaner longer, which will mean a longer life for your furnace.
Best Answer
In order for your air filters to work correctly, they must be the exact size made for the filter box otherwise yes, dirt, dust, etc. will get sucked right through the gaps. Even if you were to seal the gaps with duct tape, it would only last a little while before it came off. Your AC system will last much longer and be more efficient which will save you more money than the little savings you get from the previous occupants cheap fix.