Had a few from both sides of the table. I'll do the "being interviewed" ones here, and the interviewing others in another post in a bit.
Been to a fair number of interviews where an apparently critical skill (e.g. very advanced Excel, including programming in VB) wasn't mentioned on the job description. I should note that though intermediate Excel (e.g. sorting, pivot tables, look ups etc) were common for that role, that was the absolute maximum usually needed..
One where it became apparent that the company had a certain problem, and the "interviews" were really to try to get potential solutions from the candidates. There were 3 people in the interview, one of which didn't speak the entire time and just wrote down everything I said. The questions were all based on a single scenario, for a job that had many elements to it. They took copies of my notes I'd taken in with me, got me to write on a flip chart rather than the whiteboard that was there (silent woman took and carefully folded up all the completed sheets). Every time I gave a decent answer they would all 3 look at each other meaningfully and scribble madly on their notes. I contacted the agent after and commented that's what I thought was going on, and they said I had been the 4th out of 5 candidates so far to say that. They were also interviewing 10 candidates - a massive number as in that industry the shortlist is usually 3 or 4. Then they "withdrew the vacancy due to a re-organisation" the day they'd spoken to the last candidate.
One where I had aced the telephone interview (days before Skype, teams etc were around). Was told they needed to do a very quick F2F just to ensure "you don't have multicoloured crazy hair, and aren't covered in visible tattoos & piercings", as they had rather staid old fashioned clients. I am short & fat, and rather plain. Went into London in a very smart business suit, 2 inch matching court shoes, hair neat and tied back, very light make up, tan tights, new matching handbag etc - perfect for staid & traditional companies. Walked into the hotel lobby we were meeting at, they looked at me as I walked over to greet them & I could see their faces falling. Meeting lasted all of 10 rather awkward minutes - I didn't get the job.
Interviewing for a national financial services company, for a project management role. Was enthusiastically talking about the importance of accurate record keeping, version control and audit trails (part of the job) from both a PM point of view and a legislative point of view, and they were completely dismissive of the entire subject. I called the agency from the car park before even driving home to withdraw.
Most recently, interviewing for a local government role as admin but in a testing area. It had been made clear that there would be some need for collecting & delivering samples around the county and surrounding ones, which I was fine with. Sadly I tested =ive for Covid that morning, so obviously couldn't attend but they were keen to still talk to me so we set up a Teams interview for later that day. Early on in the interview I checked that there would be no heavy lifting etc as I have a bad back and left leg - this was fine. We got to the bit where we were talking about the travel requirements of sample delivery and collection and 2 requirements suddenly appear. Firstly that "out of county" trips may involve staying away for the night, often at short notice. Secondly that I would need to drive their (manual) van due to the size of some of the samples. I said that this would be impossible for me, as a) I need to be very careful what vehicles I drive due to my bad back and b) my bad leg made it exceptionally painful to drive a manual car (nerve damage in the left foot). As this was the case, rather than waste everyone's time maybe we should terminate the interview. They were very miffed that I didn't want to continue the interview despite there being no way I could do the job. They also made sarky remarks on the recruitment website for this local authority about me terminating the interview.