Me and the three guys in my gaming group have been collecting minis by the case for a long time now. (the both of them since Harbinger - I got the bug with Deathknell)
Not too sure what the count would be - but it has to be over 35 cases between the three of us.
I think the number of times we have gotten dupes of rare in the same case has been about 3 times. That happened before Deathknell, when the rare ditribution went to 24 a set and dup rares within a case became a very odd and rare event.
It does happen - but it is a very low chance I think. They are packed not to dupe, so it's a case of human error - not random chance.
And yes - a case should give you all commons and uncommons. Given the fact that uncommons are exceedingly useful (and in recent sets often large) this is mighty handy and a preferred way to buy.