Thanks for those tips Mike. You don't seem too Grumpy to be honest 
Great tutorial, thanks for that! I need to brush off my math skills a bit, but the explanation make it very clear why the power supply to the IC's is probably not very smooth and will be even worse the further you go down the chain.
Unfortunately I do not have 7 capacitors laying around with equal values, but I had 3x 10uF and 4x 100uF so I tried that to see what effect it would have and though the behaviour was even more erratic (as expected), the LED's on TLC's 6 and 7 do light up as bright as the rest, so it looks like adding the de-coupling capacitors saves my bacon.
Thanks again, to be continued...