If your facility is anything like many of the industrial facilities I have worked with in the "real world," then common GD&T problems might occasionally turn into a "free-for-all."
A machinist looks at a part drawing a certain way because of how he or she sets up the machine in order to make the part. The engineer views the part in a perfect CAD world. And the quality inspector is trying to re-create the drawing to confirm that each feature is correct, when measured exactly as the drawing "calls" out each feature.
The challenge for your facility is that individuals of many different GD&T knowledge levels must not only co-exist, but work toward a common goal without losing their minds. I suggest a simple, yet highly strategic Five-Step process to follow.
1) Define it
2) Find it
3) Plan it
4) Test it
5) Measure it
To begin, I would create a brainstorming group of four to five people from as many job functions as you have in your equation. A nice blend would be an engineer, a machinist and two inspectors.
Did I forget anyone? Yes. Always include someone from your management team. It will save a lot of explaining later.
The first step of the investigation is to define the GD&T characteristic.
There are many sources (or references) you can obtain if you don't already have a GD&T reference. According to my colleagues at Technical Consultants Inc., parallelism is defined as the condition of a surface, line, or axis, which is equidistant at all points from a datum plane or axis.
What is really helpful for the team to look for within the definition is the "this on the drawing means this on a part" explanation.
Once the definition is clear, the team should be able to find the characteristic on one of your part drawings. The natural response now would be to measure your part but I don't recommend this just yet. If you measure now and your reading doesn't come out like you think it should, you're right back where you started: Is the part bad, is the proposed measuring method incorrect...