What is the legal status of conventions?
Conventions, like clubs and other voluntary associations, appear to fall into the class of "unincorporated associations". This means that in legal transactions they must be represented by their authorised office bearers i.e. the committee members e.g. when opening a bank account. It's important to note that conventions are not, like incorporated companies, full legal entities with entirely separate status in law.
This is probably only of practical relevance in two areas: bankruptcy and tax. Cons may incur liability for causing damage or distress e.g. for smashing up a hotel, or causing someone to break their leg, or for debt, if they fail to make enough profit to cover their expenditure (bankruptcy). If a convention is sued for any such liability incurred, all the committee members, as de facto partners, will be jointly and severally liable i.e. each or just one committee member could be sued for the whole debt. (In the latter case, the unfortunate scapegoat would in his turn have the right to sue each member for his proportionate part of the debt - but that would be small comfort, knowing the finances of fans!) In truth, one can't really imagine anyone suing a convention for personal injury or loss as it would be much easier to sue the hotel in whose premises it occurred, and the committees tend to settle up privately with hotels for broken furniture etc. Real problems can only be imagined in the case of bankruptcy. It seems possible that any one committee member could be sued for all the debts of a bankrupt convention - not a nice position to be in. You avoid this by incorporating the convention as a limited company, in which case the company itself is liable - the individual committee members could not be sued.
But incorporation is potentially expensive. It takes a minimum £50 to be registered in the Register of Companies and the preparation of various documents, for which you'll probably need a lawyer (unless you can find a fan who's more certain on company law than me). Such a company should probably be limited by guarantee, like the BSFA - this means that the company members i.e. the signed up members of the convention, will not actually have to pay money to form the company (in addition to paying to join) - they will just have a contingent liability to pay a certain amount (say, £1) should the convention end up unable to pay its debts.
The other main area to consider is tax. Conventions, contrary to public belief, are not necessarily charities. Charities, for tax purposes, have to be registered and of the four headings under one of which such a charity must fall, only two seem appropriate for cons: "the advancement of education" and "other purposes beneficial to the community." I've no idea whether a con does qualify under these headings - but I do know that just not intending to make a profit isn't enough per se. So if cons aren't charities and therefore exempt, can they be taxed on any profits they do make? Answer: I don't see why not. Cons don't seem to have been taxed so far because no-one's ever made very much money and no-one's thought to assess them. (Looking at textbooks, I discover that the Revenue won't tax income arising to a private individual out of a "hobby", and that legally profits made by a club funded by membership subscription are regarded as "surplus" not "income". Possibly, one or both of these 2 get-outs may apply to conventions.)
If cons are assessed (under Sch. D, Case VI, I suppose, if anyone cares) then some way or another the profit is going to end up divided between the committee members and tacked on their personal income. If you don't use your personal allowance, e.g. a student, it won't matter; otherwise it may affect your tax bill.
Caveats: These are just the speculations of one person who's studied a lot of law but never practised. I wouldn't advise anyone to take the advice as the word of God in anything seriously involving large amounts of money. Plenty of advice can be had from local tax centres or citizens' advice bureaux. I also don't know if the above is true for English as well as Scot's Law (though I suspect it is).