Now that a couple of these types of puzzle have been posted its worth list the problems that have been foreseen and experienced.
Bailey M noted "with only one question, you can only accept one answer"
and that the correct "answers will be fairly scattered"
Which have proved true.
There is also the problem that the comments fill up with commentary on the first part of the question. That when a new part of the question it does not appear in the new questions list, makes it difficult to see that a new challenge is available.
Not having an easy way to see the progress of the questions (who has answered what so far) is a pain those details aren't added to the question. Posting a community wiki with the answers together is more useful but does need to be high up the page to get seen easily. The question has the potential to get very long very quickly.
Having no way to up or down vote individual parts of the puzzle is annoying when the parts could have been posted separately.
From what I've seen of the problems I would not recommend this form if the puzzles could be posted as separate questions. It only seems a useful format if there is information in the early parts required to solve the later parts.
In the question You're invited! Now what? are some good examples of these problems. I think that question would have benefited from being asked over a shorter period of time to avoid congestion of the question and comment space. Issuing the short answer to each part of the puzzle (spoiled obviously) after a day or two without explanation and moving on to the next part might have cut down the total number of answers (currently 14)
If the verbose flavour text was trimmed that question could be reasonably well balanced. It's first and last parts providing interest to readers any time in the future with the second part only of interest to the person solving in real-time, this demonstrates the utility of the form in providing the opportunity for puzzles that are one shot (ie what is the current...?) while also providing a more durable puzzle in the other parts. This of course being the exception to 'rule' don't post parts together that could be separate.
Although I would recommend not using time dependant information in puzzles in general, here it is done well is it doesn't interfere with the other parts of the puzzle. I think I remember seeing a puzzle where a long calculation had to be performed and one of the numbers would have changed rendering the puzzle obsolete very quickly, which I think is something to be avoided.
If you want to see an example of a semi-interactive puzzle that reverted to a series of individuals look at Treasure hunt 'round the world! (prologue)
Personally I prefer the shorter independent puzzles. They can be tackled one by one or in any order. They have discrete sets of comments making things clear and easy to read and it is easy to find the correct answers.