I've had my Mini 2006 S since new. I didn't drive it much during the last two years. Recently, I noticed the driver and passenger windows do not roll down into the doors to the same depth. Here are two photos showing the two windows. Window operation is smooth and without strain or grinding. Are my windows normal? How far your windows roll down? Thank you in advance.

 

Neither of my windows go all the way down into the door. I didn't even know they could!

 

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Both windows should roll completely into the doors. It's either your window regulator or the windows were incorrectly installed in those regulators. The regulator position itself is adjustable inside the bottom of the door (10mm bolts can be seen underneath/bottom of door). It's possible the positions on your Mini don't match.

 

IDK, I bought my R53 new and it's always had the glass sticking up slightly when rolled down all the way on both doors. The glass and regulators are all original so it came from the factory like this.

OP, what do the windows look like when you close the door only slightly (not enough for the glass to pop up)? Do the gaps between the glass and trim pieces along the A-pillar and roof all look the same?
In addition to the adjustment cooper48 suggested which tilts the glass toward/away from the door jam, there's also an adjustment where the glass meets the regulator that levels the top edge of the glass.
You can also try re-initializing the regulators - with the door and window closed, press and hold the window switch up for at least 5 seconds.

 

My car is the same as mrbean's. I bought my R50 new, and I've always had that one corner of the glass that meets the top of the A-pillar stick up slightly when rolled all the way down on both sides.

 

^^^
+3
Ditto = same here.