I'm not sure I understand your idea.
About recognition of ticked boxes:

• AMC first converts grayscale images to black-and-white, applying a threshold (Edit/Preferences/Scan/Scans conversion/Black&white conversion threshold). If light grays are mis-converted to white, you can increase this value.
• Then AMC counts in each box the number of black pixels, and compares the darkness ratio (number of black pixels)/(total number of pixels) to the darkness threshold (Edit/Preferences/Project/Automatic data capture/Darkness threshold) do decide if the box is considered as ticked or not.
• AMC computes a sensitivity indicator for each page, which is near 10 (its maximum value) if in this page some boxes have a darkness ratio very near the darkness threshold. A great value of sensitivity indicates that a little modification of the darkness threshold can change the results of automatic data capture, and a low value of sensitivity tells us that a moderate change of darkness threshold won't change the results.

So sensitivity (as defined in the UI) is not a parameter that you can change. Perhaps you meant darkness threshold?
My workflow is the following:

• In Data capture/Diagnosis table, sort the rows by decreasing sensitivity.
• Click on the first row, open the zooms window and check and correct the recognition of ticked boxes.
• Move to the next row, until sensitivity is low, or until you did not change anything to recognition in the last (say) 10 rows.
• Mark, annotate sheets, send them to the students.
• Tell the students to check that recognition was OK on their sheets — and correct if necessary.

As you have noticed, the problem here is that we are not aware of "coherence problems" (two or more boxes checked on a simple question, or no boxes ticked at all) when correcting the recognition from the zooms window.
Perhaps I can add a column to the Diagnosis table with this data, but it is available only after marking.
Can you clarify the solution you propose, so I can understand it better?

Yes - so what I meant was to add the column you referred to as Diagnosis. I understand that this would only be available after marking. That would mean your workflow would require to go back to step 3 ("Move to next row, ..."after having gone through the marking.

The addition of a column (diagnosis based on coherence) would be the best solution. I simply thought that it could be subsumed in sensitivity (or in this case 'updated-post-marking' sensitivity.) so that the UI doesn't have to be touched. Of course that's not as clean a solution.

The bottom line is that I was hoping that catching "coherence problems" before my students report back from their annotated solutions will save me some work down the line. (by the way, I am looking at sending 4.8GB of mail later today for my entire class - I hope this will work out...)