Please, before I do that, let me put the question differently: is it true, that the more LEDs in a row you have in ON state the dimmer each one of those ON in the row will be?
The resistor must be in the line that only takes the current for one LED. If it were otherwise then the brightness of the LEDs would change depending on how many LEDs are on at any one time.
If you want to drive a matrix with an arduino you must use an external driver for the current source or current sink. Despite some tutorials suggesting otherwise, you will over stress the arduino by many times above the absolute limit if you try. These tutorials (one on the official Arduino site) are very bad and will eventually destroy your Arduino although you might think it works for some time eventually the Arduino will fail.
But my concern is the current flow through 595 at the top if I turn on all LEDs in a row since 8*20mA = 160 mA which is over the ~35 mA capacity of the 595.
Where do the numbers come from?
Resistors should be changed to only allow 8-9mA per output.
This is what I was working on and what I had questions about:http://sealemar.blogspot.com/2014/02/binaryclock-hardware.htmlhttp://sealemar.blogspot.com/2014/02/binaryclock-binary-clock-diy.html
Of course, the proper way to connect the pushbuttons, is to ground and use the "INPUT_PULLUP" function, but I cannot see how your project even works with the configuration as it is shown.