What problems could occur when chaining 40 shift registers?
Use Schmitt-trigger buffers at the inputs of each board. They will clean up the signals so that any noise won't give false pulses on the clock, for instance. 
The 74LVC3G17 is a triple non-inverting buffer. 

Also, pass the buffered signals to the next board. Otherwise all inputs would be parallel and you may exceed the fan-out of the driving microcontroller (I'm especially thinking of the total capacitive load). The daisy chain of clock and latch signals will give a ripple delay throughout the chain, but the data will do so as well, and you plan to go for low speed anyway.