The screen being arbitrarily divided into two halves would give away a huge plot element pretty quickly, if you are paying attention, as well as some smaller stuff. You aren't actually controlling Junpei, as you are led to believe for the entire game, at least, not really. You are actually controlling a girl in the past named Akane, who is seeing the world through Junpei's eyes. The trick is that Akane's observations are actually happening on one screen, while what Junpei experiences happen on the other. You would be pretty crazy to see the observations made as coming from anyone but Junpei, given the context, except the whole screen thing, even though there are weird little issues of phrasing that don't quite make sense, but if the game was arbitrarily played on two screens, it'd give that bit away.

There's also the part near the end where you play as Akane directly, and you play with the DS turned upside down in your hands, but that's more minor versus the fact that the entire game actually takes place on a meta level.