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Lack of confidence in CMM

I've been using the CMM for a about 4 years now in a job shop. We only use it when we *need* to (when we need to produce an inspection report for the customer). I'm the only CMM operator. Running 2012 MR1 CAD. I have several parts that I need to inspect and report on and have the same issues with, but I'll direct this thread toward one in particular.

I need to measure true position of some threaded holes and straight holes that will have pins pressed in them. I'm using the CMM currently to do an in-process inspection so the machinist knows he can run the parts. These are fairly complex parts with multiple operations. The threaded holes (measured before threads) are okay because they have a tolerance of .2mm to ABC. The pin hole (for 6mm pin) positions look strange and are out of spec. [TP|⌀.08|A|B|C]

I'm pretty sure my alignment is good. I leveled, rotated and set XYZ to Datums A, B and C (all planes). My part is up on 3 points and against a stop (repeatable). I'm taking 6 hits on 3 circles per hole and using the circles to create cylinders, then taking TP on the cylinders. I calibrate the probe every time I change it (manual). (I'm switching between 2 jobs today that both require separate probes.) I made sure my air bearing ways were clean, along with the probe, calibration tool and table.

I can post code or portions of the print if needed, but I'm mostly wondering what the general causes of error are in a CMM program? I've searched through many forum posts to find out what I could be missing in my program. The machinists never like when I have to inspect something because they don't trust my numbers. I try to verify my numbers with the height gauge, but if the numbers aren't exact then everyone has a theory (or 3) as to why things didn't come out right. Often someone will pick whichever they *feel* is better and go with that method (CMM or height gage), even if the other shows numbers out of tolerance.
What else can I do to be confident in my program and my TP numbers?

Any help would be greatly appreciated.