If you don't have a Cadillac shop manual for your '73, that's the best place to start. A FACTORY manual, not Chilton's or something. I believe the factory manual has a step by step diagnostic procedure too. I believe it was Robinair that made a diagnostic tester for the programmer and vacuum system. I have seen them on ebay, so you may consider one of these if the source of the problem is not obvious.
First make sure that your engine thermostat is not stuck open, or missing completely. It will take forever to throw any heat if the radiator is doing max cooling. Is the fan clutch locked on? Does the engine roar when you drive it, from the loud locked up fan clutch? This would super-cool the radiator, reducing heat.
Are the water lines to the heater core BOTH hot to the touch, when the engine is warmed up? There is a water valve in the system, connected to a hose near the firewall. Vacuum closes the valve, so if no vacuum, water should flow through it to the heater core. Of course you have to have the control set to heat, and the knob turned into the red area.
I believe the default setting for the vacuum is to defrost, and you should hear the flap open and close while moving the lever between heat and defrost. Also, in defrost, the default is for the blower to come on at full speed. If you never get a full speed blower, no matter what, the blower relay may be bad or have a burned electrical wire, as it draws high amperage. Look for scorched insulation on a thick wire, probably red in color. Don't worry about the a/c compressor at this time. It's not contributing to your problem, although technically it does come on during the defrost mode, so be sure to pull the electrical plug off the compressor clutch.
These are all off the top of my head. Hope something helps. Tom