To be able to check what happens, I need the steps to reproduce it.
What is the error value we are talking about?

I oftentimes use the magentic tool to properly place parts, then I duplicate and move along the needed axis on the medium grid. After building a larger model, I found that many parts were off by two small grid notches (0.4), even though I have not moved them on the small grid.

Do you mean the snap tool?
Did you use the gizmo to locate/rotate?
0.4 is quite a lot for translations. Any issues for rotations?
Does the offset appear later or when you deselect the part/group after being moved?

Yes, the snap tool.
Yes, I used the gizmo.
Not seen a problem with rotation.
To deselect, I press 'a' or click were no parts are to avoid accidental movements.

I really don't know because this part of the code has not been changed at all with the last update 😛
Maybe there is something new that collides with it.

I'll keep an eye on that and report, if I should find a reliable reproduction scenario.