I agree some of english dubbing in anime is very poor. I normally watch subbed versions of anime. Though, I like the orignal English dubbing and music (Funimation version) of DragonBall Z more than the Japanese version :)
On a slightly different note, whilst trying without success to find the actress's name on IMDB, I just found out that the film's director Satoshi Kon tragically died of cancer 5 years ago. We lost a film making genius.
You are right though. It's hilarious and somehow still follows the plot pretty well.