When plugged in and fully charged my battery can (and does) fluctuate between 100% and 96%. The reason for this is that these li-ion batteries have overcharge sensors built in that when they are full have an internal switch that allows them to fluctuate at the top range, discharing a small amount then gaining, etc etc. If you call Apple they will tell you the same thing, it is completely normal.
As far as your battery discharging very rapidly, either it is less than you were expecting, or you could have a problem. On a full charge, how long is your battery lasting? Screen brightness settings? Which model book do you have? etc etc, fill in some blanks and perhaps we can help out a little bit with some info.