It is not infrequent to see controversial reviews of specific kinds of answers in the Low Quality Posts review queue. Those answers are often short, made at most of a few commands or links with few to none words of explanation; they usually fail to provide a solution to the asker's problem (e.g. propose a tool not suitable for the job) and/or are not just slightly wrong (e.g. cannot be corrected by changing an option to a command).
To be clear, I'm not referring to the (many) answers reviewed in the LQP queue that are easily identified as variants of "not an answer": gibberish, link-only, "thank you", comments, new questions, "I have this problem too", details from the asker that should be added to the question, question bumping1.
These categories are collectively defined and addressed, among other places, in the Help Center, in the guidelines for reviewing on Meta Stack Exchange, on Meta Stack Overflow (with nice examples) and as the "recommend deletion" canned comments2. The prescribed action is quite unambiguously to delete or recommend deletion, there is not much disagreement around them and their review usually doesn't pose much of a problem.
Now, apparently there is strong consensus that we should avoid deleting poor and wrong answers, as stated on Meta Stack Exchange (Guidelines for reviewing low-quality posts, How to handle low quality answers in LQP queue?, "What are the criteria for deletion?" in the FAQ article about deletion, When should I delete an answer?) and Meta Stack Overflow (You're doing it wrong: A plea for sanity in the Low Quality Posts queue).
Along the same lines is also the accepted answer to When to vote to delete an answer? on Meta U&L, which this question looks tightly related to.
On the other hand, many posts seem to somehow advocate deleting "low quality answers", and some users in our LQP review queue show a similar sentiment.
From the guidelines for reviewing low quality posts:
[A] Answers that fail to address the question: If you evaluate the answer such, first check carefully whether there is a lack of clarity in the question that you and the answer’s author may have interpreted differently. Otherwise recommend deletion. Leave an explaining comment in both cases.
In Shog9's words:
Does that mean these answers should forever hang around the site? No, not necessarily - if it turns out they're just not that useful, they should probably still be removed - or at very least, down-voted so that they rank below other answers.
In Undo's words:
Only if you can't plausibly imagine anyone putting in the work to fix the post should you opt to delete these kinds of answers.
Also, the answers to that question outline some reasons for deleting certain kinds of answers that are "low quality" without being "not an answer".
"Wrong" as in "completely unrelated to the question"? Go ahead and delete those.
All this outlines a grey area, which stretches between deleting only those answers that cannot be read as an attempt to provide a solution, no matter how useful, and deleting anything that unsalvageably fails to convey useful information.
What criteria do you follow when reviewing low quality answers? Are there answers you think should be deleted despite not being "not an answer"? Is the LQP review queue a suitable place for such a cleanup work?
Being able to agree on some specific guidelines for our site would be beneficial to reviewers (less work for them in the queue), to answerers (a more clear message on what they did right/wrong) and to all users trying to learn the art of reviewing.
2 Link-only answers have been addressed on Meta U&L, too.