It is a sampling scope, which is set in the dot mode, instead of the vector mode. One can see the individual sampling periods as individual dots on the rising and falling edges.
To me, like Mike suspects, it is a problem how you are triggering the scope.
If you have a 4 channel scope, use Ch1 for the slowest counter, Ch2 for the next counter, and finally the Ch3 for the Ch1 AND Ch2 output.
Trigger from Ch1. Adjust the timebase such that you get integer clock periods and thus a stable display.
Also...decouple the 8.0 Mhz oscillator. Protoboards are not good for high frequency circuits, and I strongly suspect that you may have noise which is falsely triggering the counter. That will completely screw up your count.
As a matter of fact, there is A LOT OF NOISE, which one can see as dots jumping high and low.