Question: Is there a report to run so we can see which operator completed a certain manufacturing operation on a manufacturing order?
Answer: Yes, you can see this in the Product Report, accessed from Reports > Product Report

Or the Product Report dashboard button:

You can view product reports by Part Number & Serial Number or by Order Number. You can change between these by using the Serach By drop down menu:

Once you've selected the order number, the full product report will load.

This shows a break down of each manufacturing operations, and which operator completed each stage.