I've shown my circuit design to a friend who really knows about electronics. HE had two remarks/questions:
Will it not be a problem that the SCK and SS signals coming from the Arduino are connected to 9 shift registers? He says that the SCK and SS signals are probably carried by weak currents (10-20 mA) and if this gets divided into 9 parts, it might be a problem. He also says that he looked at the datasheet of the TPIC6B595 shift registers and that they can work with very low currents, so maybe it's not a problem after all. I thought I'd ask your opinion anyway, just to be on the safe side. According to my friend, if this is a problem, I could employ some buffers like the 74HC125 in order to get around the problem, but I'm not sure what that means in our case.
What is the frequency of the MOSI/SCK/SS signals coming from the Arduino? It seems that if the signals have a high frequency, the circuit design becomes more complicated. Now, I'm sure that the signals cannot be faster than 16 MHz, which is the CPU frequency of the Arduino, but I wonder how high is the actual SPI frequency. If it is too high, do I need to take into consideration some additional things? He mentioned something about impedance, but that's a bit high-level for me at the moment...