Empirical Engineering Answers:
Yes: you will save electricity costs by running your blower on low.
No: you will not save on gas/oil costs by running your blower on low. Because the slower air velocity over the heat element is transferring fewer BTU units into the circulated air and they simply go up the exhaust pipe.
The NET difference of the above two figures is your savings or cost.
I am currently heavily invested in studying and learning the subject as I commit myself to reducing my winter energy costs this year.
With heating oil at $4.50/gal I can assure you without measuring anything that running my blower on low is NOT more efficient from a $$ perspective. I'm in the process of re-wiring my blower to run on high with the furnace. In support of this: I found the mfr owner's manual for my furnace and in it, it states, "if you have an air-conditioning coil installed, you should switch the furnace blower speed to high to accommodate the decreased air-flow caused by the cooling coil in the plenum."
I have also measured that on low speed my furnace requires AT-LEAST 1 hour of constant running to raise my home temp by 6 deg F. On high speed it takes 30-40 min. With a one-gallon-per-hour burner nozzle that saves me AT-LEAST 30% on fuel oil plus another 20-30 min of blower run time or at least 30-50% run time savings. Now, I haven't done the measurement to learn how much electricity my blower uses on low vs high. But I'm reasonably sure it uses less to run on high vs low then it uses to run on low vs OFF. I do know that my entire furnace runs safely on a 15amp breaker with the blower on high, the burner running, the humidifier running, and the water pump to empty the humidifier running. Thus, my blower can't be using that much electricity on high.
So clearly, running your furnace blower on low is only more efficient IF-and-ONLY-IF the cost of the heating fuel is much much less then the cost of the electricity to run the blower that little bit faster.
Best Answer
Look for cold spots in your home. A room that tends to stay cold, despite your attempts to keep it warm is a signal of trouble. A nice tool for all such problems is the hand-held thermal sensor you can now buy, like this Black and Decker Thermal leak detector. Just aim it at a spot on a wall, ceiling, etc., and click the button. It gives you the temperature. Now move the sensing spot around, and look for cold spots. This can tell you if you have missing insulation in a wall cavity, or a spot of cold air entry into your home. Use this to decide to add weather stripping to a window or door for example, or to inject foam insulation into a deficient wall cavity, or simply to help you balance warm air flow through your heating system.