I set temp to 74 and stop at 70 and decresing.

Looks like you have a hold function. This will bypass the programming and "hold" your desired temp. If the temp rises but reaches a maximum of a certain degree than someone has set the maximum heat temp to that degree. Meaning you will have to enter the settings menu and scroll through to make the changes. You need the manual. Good Luck.

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The old white-rogers thermostats with a mercury switch are adjustable. snap the face off. In the center you will find a plastic slot screw. set the indicator to the actual room temp.
Other type ? Replace the thermostat

have you checked the filter ? do you have the temp set to low? are you trying to cool to big an area? shut it down again and let it thaw out. set the stat to mid range and trun it back on. close all unused rooms. when the unit cycles of and its still not cool enough turn the tstat down unilt it comes back on and leave it there.. unil the rom temp reaches 72-74 degree. thats the best set point .. you might be about to get it down to 70. but my bet is 1 dirty filter. and set temp to low.

I think, the heating sensor misplaced or defective.If it's placed in right position, may be short. Please replace the sensor.Helpful?

themostat is bad, or the heat anticipator on the stat is bad, which means you still need a new stat

When the thermostat calls for heat it should run until the room reaches the temperature setting then shut off. Is the blower motor running and can you feel air coming out of the vents? It sounds like the blower is either not running or putting out enough air to keep the furnace heating. The blower moves the heat from the heat exchanger to the room, if it can't remove enough heat from the heat exchanger there is a limit switch that will shut the burner off if it gets to hot and that's what it sounds like is happening.

The only thing I can think of other than being just old and worn out is that by design it may not be set to run but so much at a time. Has this always done this since you have had it? It may be needing calibration. One thing you can try is to set it at 2 degrees higher than you want it and then it would shut off at the temp you actually want.

Your heater might be on the Auto settings .. it will turn on and off itself once the pre set temp is reached ...

You can adjust the position of the room air sensor found on the back of the unit between the heater and the wall. It is a black rubber bulb with yellow wires. There is a few inches of extra wire you can extend higher to get a more accurate reading of room air. While you are back there, check for drafts that will give you false readings.