How should I evaluate my central A/C to see if it's working properly?
When the person you spoke to said to measure the &quot;temperature difference between the return and supply sides&quot;. What they were talking about, is what's known as Delta T (of the evaporator).  It sounds like you took the first measurement in the proper place (or close to it), but not the second measurement.  The &quot;supply side&quot; refers to the air just after it passes through the evaporator, while &quot;the return&quot; is referring to the air going in to the evaporator.
You could also measure the Delta T of the condenser, but I'm not sure how useful that is. Simply measure the ambient air around the condensing unit, then measure the temperature of the air exiting the condensing unit.  The difference in these values is the Delta T of the condenser.
There are three values HVAC technicians typically use to evaluate a system. Superheat, subcooling, and the Delta T (of the evaporator).
Superheat
This is the number of degrees a vapor is above its saturation temperature (boiling point), at a particular pressure.
Calculate Superheat
To determine the superheat of a system:

Using a gauge, measure the pressure on the low side (suction) line.
Using a chart for the type of refrigerant, convert pressure to temperature [Saturation Temperature].
Using a thermometer, measure the temperature of the low side (suction) line [Line Temperature].
Calculate superheat [Line Temperature] - [Saturation Temperature]

At 75°F - 85°F ambient temperature, superheat should be 12-15°. Above 85°F ambient, superheat should be 8-12°. Check manufacturer documentation for recommended superheat values.
Superheat too high
If superheat is too high, it means that not enough coolant is entering the evaporator. This leads to poor refrigeration, and wasted energy.
Superheat too low
If superheat is too low, it means the evaporator is being flooded with coolant. This could lead to liquid refrigerant getting back to the compressor, which can be really bad.
Subcooling
This is when the liquid refrigerant is colder than the minimum temperature required to keep it from boiling.
Calculate Subcooling
To determine the subcooling of a system:

Using a gauge, measure the pressure on the high side (liquid) line.
Using a chart for the type of refrigerant, convert pressure to temperature [Saturation Temperature].
Using a thermometer, measure the temperature of the high side (liquid) line [Line Temperature].
Calculate subcooling [Saturation Temperature] - [Line Temperature]

Subcooling should typically be around 12-15°. Check manufacturers documentation for recommended subcooling.
Subcooling too high
If subcooling is too high, it means the condenser is flooded. This could lead to the compressor working too hard, and possibly being flooded with liquid refrigerant (which is really bad).
Subcooling too low
If subcooling is too low, the refrigerant can &quot;flash&quot; or boil before it reaches the evaporator. This will lead to the metering device not being able to properly meter the refrigerant, which leads to poor refrigeration.
Delta T
Knowing the change in temperature of the air moving through the evaporator can also be useful.
Calculate Delta T
To determine Delta T:

Measure the plenum air temperature about 12&quot; from the evaporator.
Measure the return air temperature close to the unit.
Take the difference.

Typically, Delta T should be 15-18°F. Check manufacturers documentation for recommended Delta T range.
Delta T too low
This is usually caused by return air bypassing the coil. Make sure the evaporator is properly sealed to the unit. It can also be a symptom of low refrigerant, bad compressor valves, or a leaking reversing valve.
Delta T too high
This is commonly caused by low air flow across the coil. Make sure the filter is clean, and the fan is set to the proper speed (on multi-speed units).
Diagnosis using superheat and subcooling
Knowing only superheat, or subcooling is not enough. To figure out what's going on, you'll have to use both values.
High Superheat, Low Subcooling
This usually means the system is undercharged.
High Superheat, High Subcooling
This likely means there is a blockage in the system.
Low Superheat, High Subcooling
This usually means the system is overcharged.
Low Superheat, Low Subcooling
This usually means too much liquid is being fed to the evaporator. Likely a problem with the metering device.
All values are based on my current R22 system. Values may vary from system to system, always check manufacturer documentation.