Been a while since I've posted anything SharePointy.
One reason is the migration to Exchange that I was recently involved with and it's in fact still not completed, so expect Part 2 of the post anytime soon(ish) - it will include GMail to Office365 stuff.
Now, I've found out that whenever your dates in an out of the box task list become overdue, they are NOT marked in red if you've changed the Due Date column to include the time (and not just date).
Strange, isn't it? Yes, so you can't really use this as a very precise task/time tracking solution (yet).
Default (Due Date = Date Only) and today's date = 07/04, so any task before that should be RED.
Including the time, and the task is no more overdue :) I've talked to MS about it, and hopefully it will be changed in the future by the product team (which happens to be Project for that one).
So... alternatives are for you to use some list conditional formatting...which is another big topic I might write about in the future as I've had to do it as part of a project management solution.