economy mode question
There is probably not much "coolness" remaining in the coil when the compressor shuts down, but when the fan shuts down, you are shutting off a rather large motor (many 240 volt AC units can have 1/2 horsepower or larger motors) that can be pulling a few hundred watts. If there is not a need for much cooling, for example at night, the "economy mode" button may make a big difference because the fan isn't sitting there "coasting in neutral". If the AC unit is running maxed out where the compressor is staying on most of the time (and the fan too), it is not going to make much of a difference.
One problem with running the economy mode however is if you live in a humid climate, you may end up with a "dirty sock smell" on the coil. This is because the coil remains wet with condensate when both the compressor and the fan shut down at the same time. If the fan stays running, the coil gets a chance to dry out between compressor cycles, and thus keeps bacterial and other germs from growing in the dampness.
On a convenience note, if this air conditioner is installed in a bedroom, the starting and stopping of the fan may get annoying and wake you up. I have been in hotels before where the air conditioners are configured to stop the fan like this when the cool or heat need is met, and it drives me crazy. I frequently pull the cover off and re-configure the unit to run the fan continually (this has gone un-discovered too, as I stayed in the same hotel room a year later, and the AC unit was still set this way!).