In general the voting system can guard against false positives or false negatives. By that it can either bar legitimate voters or allow illegitimate voters. Since the USA has a historic tendency of barring the poor, minorities and women from voting; elections officials should take that into account when considering trade offs.
From an election integrity standpoint, the modern implementations of vote by mail is little different from electronic voting.
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The jurisdictions that I'm aware of scan AND tabulate ballots as they are received. This permits peeking at early results. Citizens expect that votes are not tabulated until polls close on election day. Administrators argue that the pre-scanning and tabulating isn't really a count and that only the final report is a count.
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Until very recently, vote by mail lead to a novelty participation bump followed by a long decline. Explained by losing the culture of voting. Postage is now prepaid in some jurisdictions, which may have lead to a +4% boost in participation, matching prior poll site participation rates. But it's too early to separate the prepaid postage boost from the overall boost in 2018. Time will time.
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The transition to vote by mail is driven solely by appropriations (pork) and administrator's desire for centralization.
With vote by mail comes new business models. Whereas with poll sites we'd only pay per ballot to accommodate projected turnout plus 10%, we now pay for every voter every election. Vote by mail ballot packets are ~$2 whereas poll ballots cost ~10c. Additionally, all new tasks like signature verification and ballot tracking are new opportunities for rent seeking. Again, per voter per election, vs time & materials.
There's all new gear to buy, of course. One could argue this is no different than any other IT lifecycle.
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Another way vote by mail is like electronic voting is the complete loss of voter privacy (the secret ballot). Elections are administered per precinct. Received ballots are binned. So very likely that your ballot will be the only one from your precinct in the bin. To protect the secret ballot, ballots must be sorted into precincts before processing (opening). This adds considerable effort and expense to the entire process (logistic nightmare). Last time I checked, my jurisdiction still was not doing the legally required precinct presort.
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Because voters are no longer able to fix their own errors (like with the mark sense poll based systems mentioned elsewhere), administrators have to adjudication voter intent. Now that ballots are optically scanned as they are received, like a fax machine vs the mark sense systems, voter intent is adjudicated electronically, meaning there's no paper trail. Makes the manual recounts and audits kind of tricky, if not completely suspect.
You state many other things in your comment that are incorrect. For example, if I make an error on my mail-in ballot, I get a new one... just like the instructions say. That's never happened to me, because it's pretty straightforward to not spoil my ballot.
And if the ballot is marked oddly, there is a paper trail, it's... the original ballot. As you're probably fully aware, some recounts look only at ballots that show overvoting or otherwise are judged less confident by the counting system, and more precise recounts look at all ballots. It's not that tricky, and it's certainly not completely suspect.
My county uses the same system for in-person and mail-in votes.
That's almost entirely theoretical, we hope. But I'm sure there are parents or adult children or spouses or whatever that force results that they want. The North Carolina election where people were picking up ballots and marking them doesn't seem to have been repeated in Oregon, as far as we know.
I tend to be a last-minute voter and I see other people who are scurrying into the library to deposit their ballot. Or the long line of cars at the voting office.
One thing about Multnomah County, not sure of other counties in Oregon, is that you're notified (by email, maybe text is also an option) when ballots go out, when they've received your ballot back, and when they've accepted your ballot.
