This question is out of curiosity: what happens if a teacher mentions a flaw that the student has (for example, organization, time management, stubbornness) but otherwise thinks very highly of that student? (Assuming that the teacher does not criticize the student too heavily for it). How can this influence admissions decisions?
It is the exceptionally rare individual that truly warrants a recommendation (and once you get a job, a year-end review) that states that the individual has no flaws and nothing that they need to work on. An AO would probably put more weight into such an honest rec than one that say that the sun shines out of the applicant’s butt.
Of course, it depends on how the flaw is described and the tier of college you want. Organization and time mgt can be darned important for a top college.
I wouldn’t put it quite as colorfully as @skieurope, but when I was being taught how to write LoRs (once in a corporate setting and again in an academic setting) it was emphasized that including some negatives that are not significant to the thing being applied for, and/or that have been largely overcome makes for a stronger LoR. The logic is that there is no such thing as a perfect person and addressing some weaknesses makes your positive remarks more credible. With students the easiest way is to talk about the growth you have seen.
There are LoRs that are bland and detached, but that’s no help. There are letters that code their concerns. “Johnny could benefit from xxx.” Adding even a light negative is no help when there’s fierce competition. Adcoms can pick up on this as a concern- not something generous. Eg, saying someone could speak more in class- it’s kind of like, why did they mention this? What do they really mean?
Imo, good ones focus on classroom performance skills and growth. Likeability. Plenty are all positive and still appear solid. YMMV.