I've just watched day 18 and what made me think was the way Casey thinks about updating each frame. So I've observed there are perhaps two schools of thinking about frame updates.
First - Casey's:
You're at time T when the frame switches. During frame which spans from T to T + 1 you're calculating what happens in game at time T to T + 1, so essentially you're trying to predict what the game state will be when the next frame switch happens. The problem I see with this way of thinking is as Casey said many times, it doesn't handle variable framerate at all, because you're PREDICTING what the state will be at time T + 1, so you cannot possibly account for variable framerate.
Second - (This is how I've been thinking about updating frames and seems to me almost every tutorial and article is):
You're at time T and you're calculating what happened to game state since time T - 1. The ugly thing about this is you're displaying state of game from time T at time T + 1. I think that this isn't real problem though, because it doesn't matter that you're offset by one frame from game time, if you're consistent with it. Benefit of this approach is, you're handling variable frame rate well, cause you always know how much has game time advanced since last frame switch.
I'd love to know what you think about this, if this is even a valid discussion and if so, what school of thought do you prefer?