ShiftPWM_invertOutputs should be set to false for the TLC5916. That was an error on my website, which has been corrected now. How many 5916's do you have connected and how long are your wires? It sounds like your clock signal is missed sometimes. You can try using the push-pull line driver to improve the clock signal.
I have only a single 5916 wired in at the moment, everything is just bread boarded right now and so the wires from the arduino to the 5916 are only about 4 cm. I'll try to add in the push-pull line driver and see what happens.