It was fascinating because I myself used to trawl through forums like TSR trying to find out what it was like, what the criteria for selection were, and how to stand out!
There were a few structured questions that we had to ask the candidates. The rest was pretty much flexible to discuss things on each candidate's CV, and it really struck me how similarly excellent most of those were. It really is tough to stand out.
More often than not, the ones who went through had done just one or two thoughtful things to show they had gone the extra mile. Things like sports, societies etc. are all very well, but everyone has those. The candidates needed something a bit extra than that on the day so the chat actually went somewhere, which I'm sure you knew already.
You probably want some examples...
My best candidate was someone who invested in the markets a bit, he really understood how to analyse company statements and performance already and really stood out. Understanding that sort of stuff really is above and beyond, but it shows there are things you can do to make sure you stand out.
I'm happy for people to PM me for a rough benchmark of where they're at compared with the general populous of applicants I interviewed, if that's helpful.
There was also one guy who had found someone on LinkedIn and mentioned he'd exchanged emails with them about the team they were in, the grad scheme etc. Anyway, he name-dropped him in the interview and it turned out I knew the bloke he was talking about! He was on the Markets scheme and we did some training together. That was good initiative. I suppose a bit lucky that I knew the guy so could be confident he wasn't bullsh*tting, but you earn your own luck, so they say.
Oh, and there was one of those abstract questions at the end - estimate how many yellow taxi cabs in NYC, that sort of thing. I think one of them was 'estimate how many cyclists commute in London on an average weekday'. It's just about approaching the problem with a clear head and logic. If people asked me for the population of London nicely then I gave them that as a starting point. I liked the ones who bounced ideas off me every now and then to check they were on the right track.
The (reassuring) truth to it, in my experience, is that there is very much a human element to the assessment. I was purely on interviews (not group exercises or such like) which the candidates had not prepared for. After two interviews, the other assessors would meet in a room to calibrate the last two candidates we interviewed. You'd then explain the case for each of your candidates, and we'd work out who we were putting through from the group.
There was no limit to the number of people we could put through on the day. I think it was in January/February time but can't remember for sure. I get the impression some places were held back so they don't all go in the October/November rush.
General advice - relax, be yourself, don't guess what the interviewer is looking for. Sell yourself as best you can, and if you don't get it - ask for feedback. Not because by some miracle they will reverse the decision due to you being so good at obtaining feedback like you said in your competency assessment, but because it's a actually very useful thing to get.
Hope that helps