(** SPOILER ALERT **)
So what nerdy EEB things tripped me up? (I should point out that none of the people I saw the movie with picked up on any of these things.)
First, the monsters that Godzilla is fighting (the MUTOs - don't ask) are referred to as parasites throughout the movie. But they never make any attempt to parasitize Godzilla, and in fact have eggs that are "laid" in the environment, not inside a host.
Second, despite referring to MUTOs as parasites, the MUTOs eat nuclear weapons and use them to speed up the development of the (external) eggs. It is explained that the MUTOs "eat radiation," whatever that means!
Third, Godzilla is constantly referred to as the "predator" of the MUTOs. But after killing both monsters in the climactic fight scene, Godzilla makes no attempt to actually eat either one. I would have thought, given how much energy Godzilla seems to expend fighting, he would have wanted something to eat.
Fourth, it is put explained that the MUTOs (and other radiation-eating monsters, presumably) headed underground millions of years ago, as the Earth's surface became less radioactive, and that Godzilla (and other "predators") followed them. The scientists actually say something like, "The Earth's surface was ten times as radioactive as it is now." But just how radioactive is the Earth's surface now? Ten times nothing is still nothing.
Fifth, the MUTOs can trigger electromagnetic pulses (EMPs) that can shut down anything electronic, but without doing any damage to anything living (not even puny humans). What, exactly, would be the selective advantage of such a trait millions of years ago? How could it have evolved?
The ironic thing is that these are all relatively minor plot points, compared to the existence of the MUTOs and Godzilla in the first place! But watching movies is always an exercise in the suspension of disbelief. The degree to which you are willing to suspend disbelief is, of course, dependent on the genre of movie. In an action movie, you don't count how many bullets the hero has fired; in a horror movie, you don't assume that the bad guy is ever really dead; in a monster movie, you don't question whether the monster is actually plausible. So when I went into Godzilla, I was perfectly willing to accept the existence of a giant, radiation-breathing cross between a Stegosaurus and T. rex that fights other, equally implausible monsters. I just wasn't willing to accept the lousy explanations put forward for the existence of such monsters!
That got me thinking: what monster movies (or other movies) do a good job with biology? One that comes to mind is Alien - there are actually some parasites (well, parasitoids, technically) with very similar life cycles (see, e.g., http://deepseanews.com/2011/05/this-is-clearly-an-important-species-were-dealing-with/). And the recent movie Contagion actually used a disease whose epidemiological characteristics (transmission rate, mortality) were fairly plausible. They even bothered to explain the concept of R0! I'm sure there are others - let me know your favorites in the comments.