The main blower on my Rheem gas furnace is running longer than it should after combustion shut-down. This is a new quirk, with nothing obvious to explain the change except normal aging. The furnace has no companion AC and no fan-only wiring from the thermostat. Combustion sequence seems to be normal, including main blower delay after ignition; but when combustion stops, the blower continues to run much longer than necessary (although it does stop eventually). Service personnel replaced the original fan limit switch, needed or not, with a new design about 4 or 5 years ago, and the new equipment has been running well until now. Should there be a set-point adjustment on the fan limit control?

Yes there is an adjustment but there are many different types of fan and limit switches.
First I will ask you is this a fan switch on it's own without a limit switch?
If so it might be this switch, If you see a place that says fan off temp, and you can move a little lever. If it is set at around 90 to100 degrees, move ut up another 5 to 10 degrees. Some time the switches get weak after all of the heat that they are in and need to be adjusted. Hope this is what you have but if it isn't maybe you can use this info to figure out the one that you have.

The main blower is being controlled by a White Rodgers 5D51-78 "fan and limit control", "single element type". On the face of it is a manual-auto mode switch which in the manual position can be used to activate the blower (and is working), but not to turn the blower off once it is activated automatically. I haven't removed the control from the furnace or looked inside it, but except for the mode switch there are no obvious user adjustments on the exterior.

I haven't removed the control from the furnace or looked inside it, but except for the mode switch there are no obvious user adjustments on the exterior.

Under the cover on most of these units is a dial with adjustable pointers/levers. Adjust as letmetellu suggested. If not buy a new control.

The main blower is being controlled by a White Rodgers 5D51-78 "fan and limit control", "single element type". On the face of it is a manual-auto mode switch which in the manual position can be used to activate the blower (and is working), but not to turn the blower off once it is activated automatically. I haven't removed the control from the furnace or looked inside it, but except for the mode switch there are no obvious user adjustments on the exterior.

If this is the fan and limit switch I am thinking about it has a case covering the working parts. If you squeese the sides of this cover it will come off. There is a round dial inside with three different setting indicators. One should be set at about 180-200 degrees, another one that is set around 145-150 degrees and the third one is the fan off position and it should be around 100-105.
To make an adjustment unplug the electric cord to the furnace, Hold the wheel with your fingers so that it can not turn and move the botton setting to about 110 degrees, put things back together and plug in the cord. Try the furnace and see if the fan turns off on it own. If it does not turn off on it's own use the handle of screw driver and tap the box, this should make the fan go off if it has been running for quite some time, if it does make it turn off then reset the bottom setting about 5 degrees higher and try the furnace again.

A dirty evaporator coil,blower wheel or return air filter will make it act that way. If you can't remove the heat from the system due to air flow restriction the blower will run longer.