I saw in another thread Keiwan mentioned he may do "linked" muscles in a future version, which would help a lot with the sort of designs I'm messing with. Just wanted to mention that if you do this, inverse links would help as well - it would reduce the outputs on this guy in the video from 24 to 6 real outputs with 6 linked and 12 inverse linked muscles.
Also, an idea I wanted t mention: genetic algorithms are fun and all, but the standard set up of running and breeding generations is terribly inefficient, and I think this idea might also fix some of your other bugs where it feels like the best of each generation are sometimes lost... Rather than discrete generations, you could kill off poor performers by wiping the contents of the least fit many times per second and remaking them as children / mutations of the most fit.
When you have generations, not only are you wasting CPU on simulating things that don't perform well, you are also selecting only for what is best for the first n seconds, rather than selecting for stability, resilience and reproducability - with "immortal" creatures, the top performers will constantly breed for as long as they remain the top performers. In running or climbing mode, you could show all, but space them out, focus the camera on the current leader and spawn children just off screen to the right, when a creature is too far off screen to the left of the leader, it is deemed unfit and flagged to be respawned to the right, so you'd always see the best of breed, running past a bunch of slightly inferior mutants, and occasionally the camera will pan right to a new, superior variant.
Also, you could implement a very simple run time mutation and pseudo back propagation: Each frame pick a creature at random, pick a weight, compare it's value to the same weight in the leader. If it is the same, add a bit of random, if they are different, adjust the weight to be more like the leader, but allow it to overshoot. eg if the weight is 0.4 and the same weight on the leader is 0.43, adjust to anywhere in the range 0.4 to 0.46 you could do that constantly - adjusting one or two weights per frame at random - things that don't work will naturally fall off and respawn, but things that do work will keep pace or overtake to become the new leader, without having to go through the birth / death cycle.
Anyway, just some thoughts, I might take a look at your code too Keiwan, I have not written a proper NN before so it should be interesting.