Chaser circuit with a chain of 4017's
You have no hard reset on the whole 4017 chain - "the dog chases its own tail" and it relies in being at least partially correctly reset to initialise.  4017s may wake up fully reset, or not. Never depend on them being reset. 

A 'Mickey mouse" way of doing this is a capacitor from the lh 4017 MR to Vcc and a resistor from that MR to RH 4017 pin 11.
Somewhat similar to what you use now on 4093-pin 13.  

Or you could formally gate the reset state.  

At the moment you unreset each 4017 as the prior one steps off zero for the first time. It seems you could just reset them all initially - as you explicitly gate the clocks with 4081's.



Peripheral:

R1 is somewhat small load wise - a larger minimum value and if necessary a small er cap may be in order.

The 4017BM is shown as having a Schmitt triggered clock. Ancient memory suggests that some versions do not have a Schmitt trigger here and that it can cause problems on slow signals. Ensure that you have the Schmitt variant.