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Quoting REP 119 — Specification for TurtleBot Compatible Platforms:

Odometry is expected to be accurate within 1% after calibration in both linear and angular movement.

So dead reckoning should be very good indeed. This doesn't answer all the questions posed, but it does give a target to shoot for. I never tried manually calibrating the gyro so I can't be sure that my Turtlebot actually had a hardware issue, but I do imagine it should have been much better than that, even with a suboptimal calibration.