I"ve never had to deal with the turn indicator bulbs on my e53 yet...but are any of them dual filament (front or rear)?
Fast blinking indicates that a turn indicator bulb is burnt out. On BMWs that have dual filament bulbs...if you have the LCM III (starts with 9/98 build date)...there is a replacement bulb feature...so if a front turn indicator bulb burns out (the high watt filament)...it will use the low watt parking lamp filament (or vice versa).
Do the lights on the side of the vehicle between the front wheels & front doors blink with the turn signals?