Well it looks just fine to me considering we have never had a "real" working mirror ever in iClone. It's always been a bit of a "kluge" to get something to work as a mirror in iClone.
I have gone so far in the past as to use the Water prop and turn a room on it's side to get a mirror reflection. A real mirror is rumored to possibly be coming in iClone 8 so we'll have to wait and see.
Yours looks great so you'll need to do a tutorial and tell us how you got it



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I understand what you did here, but while it looks good overall, it's not exactly the right way.
It seems you used cutout main camera video render and applied it to mirror props.

To make it more accurate you need to record a video for each mirror separately from the back, apply and record again so that mirror reflection in another mirror would show up.

In order to do that you need to "break" your model and have walls to be separate and hide them while recording from the back.
If your walls just are just thin planes with back faces pointing outside (normals inside), then you may disable 2-sided and camera would see through the wall from outside.

Next, you have to place a camera behind the mirror, set render resolution to aspect ratio of that mirror, pan the camera so that back of the mirror is spanned to full screen.
Next, bring a dummy cube, center it with mirror and attach camera to that cube. Hide the mirror.

Now the hardest part is to figure what lens angle should mirror camera have and track it with dummy, while main camera is already animated.
I did not spend much time here and did it mostly intuitively disregarding all optics laws probably
So I sort of tracked the mirror camera based on the main camera movements (which was already animated) by the mean of parent dummies (trackers) and slightly tweaking lens angles on the way.
All that, while trying to keep camera's full pan on the back of the mirror.
And did that for each mirror and made multiple passes so that front large mirror sees the two side mirrors and vice versa.


I do not think it is possible to get 100% accuracy with this method anyway, but with some effort and research better result may be achieved.
So here is the rig:




And this is an outcome (middle mirror came out worst, as it did not have enough tracking movements):






I forgot to mention. Mark already talked about iClone 8. Although we have to live to see if they would allow more than one functioning mirror per scene.
And also Iray, which would give you the best possible render and all kind of mirrors (that is if you have the plug-in and are willing to wait for long renders).