At smaller sites (up to 50-100 questions a day average) closing a question takes hours or even days.
- As an example, this SO question has got 5 close votes in 15 minutes, while its twin at Programmers has been struggling to get 3rd vote for over 10 hours. "Twin" here means, same question has been cross-posted at both sites, is equally inappropriate at both (tool recommendation), has comments explaining the issue for readers and is downvoted rather heavily, to -4 / -6.
Given above, suggest to take into account when there is a solid evidence that question may turn out inappropriate for the site and exercise more caution about promoting such questions in the hot list.
Penalize smaller sites questions having 3-4 close votes - say, cut their hotness score by half or drop them off the list completely. This will increase chances for less troublesome questions to enter hot list.
Indiscriminately advertising questions that are on their way to closure, with only 1-2 votes left to go hurts site community morale and dilutes the Stack Exchange brand:
watching the 'hot network questions' leads me to think that several of the recent sites are gigantic broken windows of self-absorbed subjectivity... The questions are whiney, the answers are opinion...
Consider also disappointment and frustration of new users coming to sites to ask questions similar to ones advertised in the hot list only to discover that these are voted down and closed as inappropriate (broken windows effect).
we won't tweet questions with close votes
Close votes on the question should reduce the total hotness of the question by 20% (so a closed question would have a 0 hotness score)
Weight Flags/Close Votes Against Questions... 30% of our hot questions over the past month all got closed, which is less than ideal, because we want the attention to go to good polished questions rather than works in progress... If close votes count against the hotness score, then we can vote to close while trying to improve the post, and not worry about it getting a dozen answers in 24 hours as the entire SE network flocks in.