No, we're not saying the same thing. Partly, I think you are confusing assuming that all variability falls under the guise of tolerance.I think we're saying similar things, but in your case you've described an incompatible pair of tolerances that wouldn't allow the two parts to be mated together in the first place. I was thinking along the lines of things that still fit together, but upon rotating create interference/lack of engagement points as the dimension between the two moving parts changes upon rotation.
I don't understand the mechanics of how the date wheel gets turned to be any more specific. Let's say the diameter of the date wheel has one spec, the tooth depth has another spec, the amount of variation of the diameter of the wheel has a third spec, and the hole in the center of the wheel that mounts it into the movement has a fourth spec. Similarly for the gear that turns the date wheel. The alignment of the teeth turning the date wheel can vary based on each of those tolerances. If both gears are slightly out of round, but within their respective tolerances, or slightly off center in their mount due to tolerances in the center holes, the gears mesh adequately to turn the date wheel at some alignment points, but not at others because the distance between gears changes as each of them rotates.
Or, as someone else said, maybe there's just bad gear teeth, in which case we're back to bad manufacturing and QC controls.
Variability is deviation from one part to the next, as well as deviation from perfect (nominal), due to limitations or inaccuracies in production processes.
"Tolerance" is the range of part variability that the design engineer deems acceptable for the design to fit and function properly. Tolerance is allowable variation. When tolerances are determined correctly, in-spec parts will always fit and function correctly when assembled. The acceptable degree of out-of-round or eccentricity of a gear would be one of the tolerances applied to a movement. So would limits on the variability in size, shape, and pitch of gear teeth.
If parts are manufactured within the specified tolerances (in-spec), but don't fit or function properly when put together, that's a tolerance issue. The tolerances selected were incompatible. Tolerance issues are design flaws. It's also impossible for someone to know if a failure is a tolerance issue unless they know what the tolerances of the design are.
If a failure is caused by a out-of-tolerance part, that's not a tolerance issue. An out-of-tolerance part is a bad part. The part was not produced to spec and QC failed to catch it.