I started working with 2 74HC595N to control 8x8 matrix, and found that instead of a dot it activates multiple rows. So I assumed this was due to my lack of knowledge about shift registers so I setup a simple scenario from arduino ShiftOut tutorial (single register chip and 4 LEDs controlled by number via serial input i.e. "one by one sketch". Thats when I found out that shift register has almost random values on its output pins. Some LEDs were on, some off before I started to controll them. After I turned on/off all 4 it strated to work as supposed to, but last pin retained "memory" of its state even if I reset Arduino. So my question is, do I always need to initialize every pin of every shift register (and is there an example sketch), or do I have faulty IC?
Edit: Added schematic (it's from http://arduino.cc/en/Tutorial/ShiftOut)