Hi Tobias,
Power up timer enable and insert a short pause in the start up code of your PIC to allow the serial LCD time to stabilize, .01 µF at the PIC power pins and make sure the serial out line has the proper pull up / pull down resistors as required. Pull up for data TRUE, pull down for data INVERTED. This allows the port to idle in the correct state. Be sure to provide a pull up resistor on the MCLR if you have enabled it in your config statement.
HTH
JS