The 1983 film Risky Business (the Tom Cruise one) is evidence that "boffing" may have had sexual connotations in the US, though IIRC - been a long time since I saw it - the word had to be explained to the central character and therefore to the audience as well. But I digress.
I went to my first Con in 1991 and have been going to Eastercon and Fantasycon in the UK for all but a few years from 1992 onwards. Also the 1995 and 2005 Glasgow Worldcons and the 1997 London World Fantasy and 2010 Brighton World Horror and I'll be at World Fantasy in Brighton later this year. The only non-UK con I've been to was the 2010 Worldcon in Melbourne. So this is entirely from a British perspective.
On the diversity issue, the image of friendless geeks gathering together to dress up as Klingons (or whatever) dies very hard in British media. The conventions I go to are more about the written genre rather than media, though they do cover that, but costuming is in a minority and much of if confined to the Masquerade at Eastercon. It isn't my thing at all.
However, both recent Glasgow Worldcons did attract attention from the media and you could guarantee that someone in outlandish costume will be the one out of as many as 5000 attendees would be the one to get their picture in the paper. At the 1995 Worldcon, there was a visiting American (male) who spent the whole con dressed in a black basque, red bikini briefs, stockings and suspender belt, fox ears and fox tail. Guess who was the one who got in the local paper? That Con also had an article from a local paper about someone who wondered in, paid the day membership thinking it was something to do with Star Trek, couldn't find anything of interest and seemed to think everyone was on drugs - all written up in a local paper under the headline "Weirdos' Con branded a rip-off".
That said, SF particular does attract minority types. At a typical Eastercon - and particularly a Worldcon - I see fans who are unusually tall (less often unusually short), morbidly obese fans, disabled fans, LGBT fans and fans who would be I guess somewhere on the Asperger's/autism spectrum. I have to wonder how many of these feel isolated to some extent in everyday life. There was a Locus con report once which described a Worldcon as something like a Gay Pride march - a parading of difference. (The writer of that article is himself gay, by the way.)
As for overall membership, Eastercons did hit a slump between 2000-2007ish, not helped by a notoriously bad one in Blackpool in 2004 (a scary place, and the con was not the best organised either) and the 2005 Worldcon overshadowing the Eastercons in that year and the next, and the original 2007 Con being cancelled causing another one to be organised at short notice. That said, the three Heathrow Eastercons in 2008, 2010 and 2012 attracted record numbers, 1300+ each. The one this year in Bradford was very good. I'll be at the one in Glasgow next year. But as far as I know there hasn't yet been any bid to organise one for 2015.