LO got 2 UTI's requiring hospitalization and catheters in the last 2 years at ALF. Should the facility have treated these better?

I am Alva, the AL is able to test for a UTI and can get a "doctor" to order antibiotics but as she said, its a broad spectrum antibiotic which didn't work on Mom. You really need to get a culture done to determine the infection and the proper antibiotic.

An AL is not a nursing facility its a residence that supplies aides to help with ADLs.

UTIs can be caused by many things. Not voiding completely, not drinking enough water or not cleaning well after a BM. With my Mom, while on antibiotics she was given a probiotic which was continued after the UTI was gone. Cranberry tablets helped to keep the UTI from recurring. Its been suggest on the forum that D Mannose works well to prevent UTIs.

When elders have cognitive decline sometimes they no longer process pain or discomfort signals accurately. If your LO isn't alerting staff to smaller changes then they'd only know there's a problem when things become critical and obvious to others. My MIL is in LTC in a very well run facility and she gets UTIs often. She'll wince in pain as she lets out urine. When we ask her, "Are you having pain when you urinate?" she says no. She has short-term memory issues and cognitive decline/moderate dementia. The staff can only be expected to do so much if they can't get accurate info from someone.

You asked, "...if a better run facility with better nursing care could have done a better job?" I'd say not necessarily.
"Should they have noticed he wasn't getting better and ordered more tests?" Maybe.
"... how common is this" UTIs are extremely common in the elderly.
"...is it indicative of overall quality of care there." Perhaps but as AlvaDeer noted, maybe there is more to the story of this particular facility.

Helpperson, for the last week or so you have written us many questions, all about an Assisted Living with which you have serious concerns. Some of the issues were about admins playing good cop and bad cop, you felt; level of care issues and costs as a problem, and problems with the Assisted Living having concerns with the acting out of the elder.
You are clearly very unhappy with the care of this Assisted Living. I am uncertain if you are POA with choice to choose another facility, but I am wondering if you might think your elder would be better at another facility?
You ask now about UTI with urinary retention. I believe you were writing us about a male. I can tell you as a nurse that retention, whether from prostate issues or other reasons (many medications cause retention, also) is a serious issues with males. IF this is the male who was also acting out, and if this acting out constituted a sudden behavior change, then the UTI could have resulted from the retention and both would almost certainly have caused some acting out, and possible real discomfort and distress. Assisted Living Facilities are often just not equipped with staff to do any real nursing care and assessments.
Antibiotics as an issue.....generally the UTI is diagnosed and treated with a broad spectrum antibiotic until a urine culture comes back after some 72 hours. Then sometimes the antibiotic is changed to another stronger one that is specific for the bacteria growing in the petri dish.
I am afraid UTIs cannot be blamed on an Assisted Living. The elder may require a different placement where there is some ongoing nursing staff, if this tends to recur. Regular assisted living aids are just in no way equipped to diagnose possible UTIs, and even retention. Some males require ongoing frequent catheterization, and this isn't for Assisted Living, but for skilled nursing, SNF, Rehab where there are nurses to do this. Often Ultrasound machines are needed to assess the fullness of the bladder.
Sadly there are a lot of issues for your elder going on I think it is time to really assess if he is placed in the right setting. Medical issues will and do occur, and really are for the most part not the "fault" of a facility.
Wishing you good luck. There seems to be just a constant flow of problems and illnesses happening for your elder, one after another. I hope things get better.

Who evaluated and treated the UTI at the AL?

In general, a urine culture (not just a rapid UTI test) should be done to determine what antibiotic the bacterium involved will be sensitive to. And there should be follow-up by the treating clinician to make sure the infection has cleared.

This also assumes that the patient is able to do some management and accurate reporting of their own symptoms.

In my experience, medical care in ALs can be very "hit or miss".