I have a little experience in the field of election administration, although I'm not about to claim expertise. Maybe I merely know enough to be wrong in less obvious ways? :-)
Regardless, it seem to me that this election is ripe to be contested, a contest may well be upheld, and the whole thing re-run from scratch.
It's clear that every vote that was set aside as questionable - be it provisional or absentee - will be individually examined and decided with the totals appropriately incremented one-by-one. And it seems unlikely that those decisions will be seriously challenged. I believe the Minnesota procedures are clear enough and unbiased enough that the courts will be reluctant to substitute their judgment for the judgment of those to whom the law assigned the task of canvassing the results.
Instead, a contest would likely involve the eligibility of voters who's votes were cast and counted on election day. Elections are human endeavors and mistakes are made. Of late, Minnesota has been looking at mistakes that would have improperly disenfranchised voters. But mistakes go both ways, e.g., voters who didn't properly register but were allowed to vote anyway. Such mistakes are (thankfully) pretty rare, but my experience would suggest that they're on the order of 20-30 per 100,000 votes.
We must accept that such mistakes occur, but we'll assume they occur at a lower rate - say 15 per 100,000. With over 2.8 million votes cast, that leads to at least 420 votes cast that should not have been. And these votes cannot be un-cast since there's (appropriately) no way to identify the ballots. If the ultimate margin between the lead candidates is, say, 200 then it is likely that the candidate with the most votes would still have been the winner even if only the valid votes had been counted. But that's by no means certain. Given a high enough level of uncertainty, a court might easily rule that the election itself was sufficiently flawed that the true winner cannot be determined with sufficient certainty.
Am I wishing for this outcome? Certainly not! But a US Senate seat in New Hampshire was re-voted in 1974 and we ought not be too surprised if it happens again here this year.