^Maybe what you're remembering is the part where Harry Shearer's reporter character hears the Japanese eyewitness call the creature "Gojira" and mispronounces it as "Godzilla" -- and later, when he says it that way on the air, a roomful of Japanese tourists calls out "Gojira!" to correct him.
Although that's not really a mispronunciation. The second consonant can sound something like a "dz" in some contexts or dialects, and the final consonant is as close to L as it is to R. So "Godzilla" is technically as valid a transliteration as "Gojira," although to English-speaking eyes it suggests an incorrect pronunciation of the vowels (the first syllable should be more like "go" and the middle isn't stressed). Then again, the name is derived from the Japanese words for "gorilla" (gorira
) and "whale" (kujira
), so stressing its syllables like "gorilla" is arguably not a mistake at all. (And given the character's spiritual component, the "God" part isn't inappropriate either.) Indeed, in the Japanese films, the name was in fact spelled "Godzilla" in English signage and pronounced by English-speaking characters the same way Americans pronounce it, as "Gahd-zil
-la." So that's the official English spelling and pronunciation even by Japanese standards, so it's a bit off for the '98 movie to treat it as a mistake by Shearer's character.