The nature of online communities is such that you simply won't have access to the information that would be required to make an informed judgement about an applicant. You can't require details of their Wikimedia activities since they could simply deny being a Wikimedian (and I believe we are agreed that we don't want to restrict membership to Wikimedians only). If you know of a reason why you should reject an application you would be reckless to ignore it, but there can be no reasonable expectation on you to do any research into applicants, since such research is impossible.
The risk of lots of people joining to manipulate board elections is very real - if we had the default staggered board resignations it would be much reduced, since there would never be a majority of the board being elected at one time (barring early resignations/deaths/etc.). Unfortunately, I didn't think of that when I was trying to persuade you against having everyone resign at once, perhaps if I had, I would have been successful... Anyway, what's done is done, the best way to mitigate the risk now is to recruit as many good members as possible - the more good members we have the more bad members will need to sneak in in order to gain a majority. Recruitment will need to be one of the top priorities for the board after the AGM (it should be a priority for the current board too, but not a top one - handling setup is top).