Let me accept that I am no expert and what we have learnt, we forgot over a period.
But, I feel that, the switch used to input data needs to be modified, as the present arrangement does creates noisy spikes due to contact bounce. Generally they use a two NAND gate configuration with proper pull ups and with a change over switch..
Secondly, perhaps the input pins of unused gates of 7404 can be connected to ground or battery. This would help reducing floating gates creating unwanted noise. It has been followed in the case of 74LS73.
haven't goon through it, but you have 5 states listed. this would seem to leave invalid states possible. the intended cycle is the path listed, but do any of the invalid states connect to itself, or a path that returns to itself (eg, a second possible cycle).
basically, you might have 2 or more possible solutions to your circuit, based on the initial condition, which might be random, or favor some unknown but consistant value.