Sorry guys - those cross-coupled gates do not debounce anything.
Using the up button as an example, U5A, U5B, and U6A are the logical equivalent of a piece of wire. And because none of them have Schmitt trigger inputs, the asymmetrical lowpass filter effect of R1-C1 does *not* prevent a noise burst out of U5B and into the counter.
R1 and C1 do debounce the leading edge of the switch signal, but not by much. (1 millisecond is not a long enough time constant to clean up most switch bounce. Think 10 ms minimum.) BUT, they also slow down the trailing edge after the switch is released. This slow edge goes into a gate with nanosecond response time. While this doesn't guarantee a 5 V tall noise burst at the output, it certainly is more likely than with a faster edge.
Some counters have schmitt trigger stages for the clock input, but the gate is presenting a full-amplitude square wave burst that would sail through a schmitt input. If you want to have the same logic polarity, replace the three gates with two sections of a 74LS14 in series.
For a detailed description of how a Schmitt Trigger circuit works, please contact member # 136174.
ak