Godzilla is meant to be something like 100 m tall and between 20,000 and 60,000 tons in weight (his size fluctuates in the various films). Of course lots of people who like doing sums and talking about cubes and so on have used the mathematics of scaling to show why - duh - Godzilla couldn't really walk, stand, or even exist. Michael Dexter presents the argument here, and also brings in thoughts on blood pressure, circulation and physiology to show that a living Godzilla would variously fall to pieces, tear itself apart, have its organs turn to jelly, explode due to a build-up of internal heat... you get the picture.
I know of two palaeontologists who have made comments on various of Godzilla's physical properties. Jim Farlow, a palaeobiologist based at Indiana University-Purdue University Fort Wayne, and best known for his work on dinosaur trackways, speculated in 1998 on the foot size of TriStar's GINO. Jim noted that he'd 'probably have to log-transform the measurements to get [the data from the toes] onto the same graphs with my other data without scrunching the other points into an indecipherable blur near the origin'. He also noted that it might prove difficult to cast even a single Godzilla footprint given grant limitations and the cost of plaster of Paris, silicone or latex rubber. Sadly, Prof Farlow never published his thoughts on this subject and all we have is a message posted to the dinosaur mailing list (here).
Sauropod expert Mike P. Taylor did a bit of science on Godzilla (this time on the original, not on the TriStar creation), but has also - for shame - failed to publish his results. Interested in how much weight can be absorbed by the limb's cartilage pads, and in how big these pads needed to be in sauropods, Mike threw Godzilla into the data set to see what might happen. Godzilla's cartilage disks would not, it seems, hold up under his immense weight, and we can therefore conclude that a terrestrial biped of Godzilla's size and weight is impossible. Mike included this valuable and surprising [joke] data in his 2005 presentation 'Upper limits on the mass of land animals estimated through the articular area of limb-bone cartilage', and to his annoyance it was the one brief comment on Godzilla that earned a mention of this presentation in a write-up of the respective conference (Jones 2005). An abstract of Mike's presentation exists (Taylor 2005), though it doesn't mention Godzilla, and you can see the presentation for yourself on Mike's website.
Oh you bet there's more. Hop to it.