I found two related bugs.
Bug #1: If you change your production wheel such that it changes the approval and thus the high approval bonuses, the manufacturing/research/wealth values do not reflect the new approval bonuses. They use the old bonuses. Even if you click "Done" and then return, the old values are still used. The values using new approval bonuses are displayed the next turn, though I was not able to determine whether the new or old values are used when you click "Turn".
If the old values will be used this turn and the new values next turn, that's fine, but it's counter-intuitive.
Bug #2: The high approval bonuses impact on production values are computed differently than described in Economy 101. It is not additive, it is multiplicative. The new formula appears to be:
(Population * AllocationPercentage) * (1 + ApprovalMod) * (1 + ImprovementMod + PlanetMod + StarbaseMod + RacialMod) = Output
instead of
(Population * AllocationPercentage) * (1 + ApprovalMod + ImprovementMod + PlanetMod + StarbaseMod + RacialMod) = Output
Okay Economy 101 doesn't specify the ApprovalMod, so perhaps this was added after Economy 101 was written, and it is intended to be multiplicative. Maybe it's not a bug, but I thought I'd mention it in case others were trying to figure the math too.