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As far as regular sets go (ie. no furniture or big-boxes like that Chima combo), the current UCS Millennium Falcon does appear to be the largest box by total volume.
75192-1 Millennium Falcon - UCS (2nd edition)
54 x 45 x 39 cm = 94770 cm3
54 x 45 cm = 2430 cm2
The original UCS Millennium Falcon box was actually larger in 2 directions however, though the ...
13
Maybe straining the definition a little (although not too much, as at-least some of them did come with LEGO pieces), LEGO has in the past sold furniture.
I think all of these items were shipped disassembled, and I can't find much information on exactly how large the box they came in was and can't be sure what I did find is accurate, but I would imagine one ...
10
Straining the definition a little less than Alexander, some of the First LEGO League challenges came in boxes with the mat folded, making the box unexceptional, but some came in boxes with the mat rolled up.
According to bricklink the 2015 challenge came in a box that was 117 cm long. That is quite a bit more than any of the dimensions of the Millenium ...
5
I thought that promotional boxed sets were good candidates for the smallest box as well, as I own a 1630-1 Helicopter (which, incidentally, I got as a promotional gift for buying toothpaste at some point in the 90s IIRC), at 7 x 7 x 4.5 cm (220cm3/0.22 litres).
There are sets with similar dimensions as well, such as 5018-1 Gravity Games Promotional Set at 7 ...
4
I would suggest looking at a speed build of this model and comparing the placement of pieces with that of your own.
So, let's try...this guy's video => The Austrian Lego Fan seems to have banged out a step by step build of this model, which shows a many angles of the area you're have issues with.
To get those butt-dragging results, you may have got your ...
2
As with “biggest”, smallest also has different definitions (weight? Width? Volume?). Here are a few candidates:
5005250 Party Banana Juice Bar - 8 x 4.5 x 11 cm (the Chicken version also qualifies)
600-2 Police Patrol - 9.5 x 5.6 x 3.6 cm
I don’t have a link or box picture, but the Dutch store opening gift Windmill comes in a pretty small box as well.
...
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