Please let me know if it is more efficient to have the blower fan on continuously rather than in the automatic position. If so, does it make a difference in heating mode or AC mode?

CAC is Constant Air Control in HVAC terms. It is always more efficient to turn a motor OFF when it is not needed. Now on the other hand sometimes you can leave the motor run to help circulate the air for electronic air cleaning ETC. The choice is yours.

I have an electronic air filter in my home and I run the fan non-stop year round. It cost little to run and filtering the air is important to me as my allergies play havok with me most of the year. Otherwise, it purely a matter of comfort. In the summer, the air constantly moving makes it seem more comfortable. In winter, it may feel drafty to some when the furnace is in the off cycle...

If you decide to leave it on - remember you'll have to service the air filters much more frequently and frequent lubrication of the blower motor wouldn't hurt either...