Is it correct to place the base to emitter resistor in a BJT circuit as follows?
The only reason I can think of for R41 to even exist is to add some threshold.  R3 and R41 creates a voltage divider, the transistor won't turn on until the voltage over R41 exceeds ~0.6V.

Moving the resistor to the new location would remove the threshold.  It could instead result in too little current flowing to the base.

Furthermore, there is no need for a pull-down resistor in this circuit.  If the input to the base is floating, it won't conduct.  If there is a long wire or a FET.