How about we leave the system as it is and apply a yet-to-be-determined amount of negative reputation for each rejected edit?
From what I understand, there is a ban in place for editors who get rejected too much. Could we have some stats to know the Approved/Rejected ratio? Depending on this, we might want to make the ban perequisites harder on the editors (or not). I also wonder the proportion of skipped reviews, that might indicate the amount of edits perceived as borderline.
Too minor is quite subjective and there are many edits that are borderline. Wherever you put the border there will always be borderline cases. Even if it means larger review queues (and yes, I know I am not a reviewer as of today), I feel somewhat satisfied with the idea that a human is going to review my edits and not some robot executing a set of not-necessarily-well-thought rules.
I think the restrictions you suggest are more likely to make helpful editors a hard time rather than really improve the situation.
And to get back on the subject of tags, which I find very important, it doesn't matter if that's a one tag change. If the question needs retagging, I feel it should and will be retagged. It is a matter of doing things the right way.
For me there is no automated way to detect a bad edit except for obvious ones. Trying to detect the others will only increase the number of false positives.
Plus I think my proposition adds value to the work of the reviewers because they would know that their review carries more weight. On the other hand, the editors would be more careful and those only striving after easy reputation would think twice (and I'm not sure there that many of the latter).
EDIT:
Now about bad reviewers:
Isn't it why multiple people are required to approve an edit?
Maybe, then, increase the number of 'Approve' votes before actually approving edits?
Or, punish reviewers who voted 'Approve' on edits where all other reviewers voted 'Reject'?