Why do some of my signals 'shiver' (have jitter)?
This looks like signal jitter to me. The clock period is minutely varying, enough that the persistence of the scope is making the edge look 'smeared'.

I don't know if your Rigol scope has the capability of calculating statistics when it measures. If it does, you can adjust your trigger point so that your trigger edge appears on the left edge of the screen, adjust the timebase to show a complete period and measure the frequency variation over time to get a feel for the variation. (Jitter can look worse than it is when the trigger edge is offscreen.)

If you want to narrow down the sources of jitter, I'd start with the RC oscillator. See if you have an option to use a different clock method (like a crystal), implement it and remeasure the jitter.