Shift registers

Other Hardware LEDs and Multiplexing
2
  1. Get rid of the cap.
  2. Put a 0.1uF cap from each device's Vcc pin to Gnd.
  3. Fix your code to output 2 bytes every time you want the output updated.
void updateShiftRegister()
{
   digitalWrite(latchPin, LOW);
   shiftOut(dataPin, clockPin, LSBFIRST, leds1);
   shiftOut(dataPin, clockPin, LSBFIRST, leds2);
   digitalWrite(latchPin, HIGH);
}

and keep the data you are sending out in leds1 and leds2