Despite all the criticism, this version of Godzilla's maneuverability and guile is impressive to say the least.
The whole 'Godzilla falls to Missiles' really isn't a detraction. The kind he was up against is one of the strongest conventional missiles, able to sink a warship with just one missile. He took twelve. SO in a way its a Dying Moment of Awesome.
This Godzilla really is quite a decent kaiju in its own right — durable if not actually entirely immune to human weaponry, strong enough to cause major destruction to anything in its way, surprisingly quick and agile, and thanks to the hermaphroditic egg-laying poses the threat of creating more of itself. If it wasn't for the part where it's supposed to be Godzilla the monster itself probably would have had a better reception (and indeed, countries with less of an idea of what Godzilla is supposed to be did tend to think better of the movie and its monster).
Really, while the movie does have its flaws, if the filmmakers hadn't named it Godzilla and had given the beast its own identity, it might have been more well-received.
The helicopter chase is easily one of the best remembered moments of the film.
Animal actually chasing down Godzilla, not only managing to catch the creature on camera but also survived being stepped on.
Audrey, Nick, Animal, and Phillipe calling in an air strike directly on their heads. Made doubly awesome in the fact that they had to contact the military by cutting into live TV coverage, making it Audrey's first (and at that point, likely LAST) TV news reporting appearance; and that it rubs it into the military's nose that Nick was right about the nest all along. Further awesome that if they hadn't done so the human race would likely have been extinct in a few years.