It's explained on the DVD... but here's someone else's write up on it.

"...this effect was done by the compositing of two different shots. First, the crew filmed Ellie running up the stairs, around the corner and into the bathroom, dollying in front of her. As she reached a pre-determined mark, she reached up with her left hand as if to open the bathroom mirror. Next, the crew filmed Ellie's hand reaching past the camera to open a bluescreened cabinet/mirror. With this shot composited onto the first shot, you get the reflection effect without actually seeing a mirror. Then, the effects team constructed a completely artificial, computer-generated cabinet and matched its moves to Ellie's hand, even including the bevel on the edge of the mirror. On the separate audio track of the DVD, the effects supervisors discussed how the shot was created. They mentioned both the bluescreening of the foreground (meaning her hand) and the fact that the mirror was completely fake. They also mentioned during her run up the stairs that the crew had "painted" out a cameraman's shoulder that appeared at one point in the scene.

It is obvious upon viewing the scene in slow motion that the hand in the mirror and the hand in the foreground are not, in fact the same. There are certain points where it is very obvious that the fingers are in a different position. In addition, the mirrored cabinet, when it opens, does not reflect correctly according to the laws of physics. The picture of Ellie and her father that is visible when the mirror swings closed would have to be visible when she opens the mirror, but it is nowhere to be found.

It is also interesting that the shot of the reflected photo lasts no more than a second or two, with a very quick fade to white before the mirror swings back far enough to see that the door is not visible, with the picture in its place. In short, this effect is very complex, but easily accomplished because the whole sequence is a very short piece of film. Some minor flaws are allowable since the audience usually won't replay an effect in slow motion in order to see them. In fact, most people who see this sequence for the first time don't even realize a special effect has taken place."

I guess it's a cool effect, if you notice it. But if you notice it, then you're thinking about how cool the effect is, instead of what's happening to Ellie. And most people won't notice it, so why not just cut away to the cabinet when she opens it?