That's one of the things I was worried about last year when I had a go at making one of these cubes. I solved the problem by making two design decisions:any reason for using the 595 instead of say, MAX7219?, maybe it is camera issues, but have seen lot of flickering with shiftregisters when creating 8x8x8 cubes, but that might be other things of course..
1 - Run the update process in a seperate thread. This way it is always in control of the data transfer to the shift registers.
2 - Turn off the power to the LEDs when the shift registers are being updated.
There's more information in the Wiki if you are interested.
Regards,
Mark