As for whether it's racist or not - I'd have to say it depends. Apparently it's supposed to be a comedy, and the scenes that many people complain about as being racist are the ones that are supposed to be funny (a call-girl with bad English, and an over the top talk show host). While I was watching it, I didn't find the movie particularly humorous - in fact I don't remember laughing, just an interestingly paced movie about being foreigners in an alien culture. Of course, my perspective is probably a bit different since my knowledge of Japanese culture, though limited, is probably a bit more than the typical American. Now, if you were watching the movie, thinking the scenes were meant to be humorous, I think then yes, it is racist. Instead I just saw them as vignettes, showing how different the Americans were, and just how different of a culture they were in.
The NYT article is interesting in that it presents the perspective that by not developing the Japanese characters, and instead emphasized their "otherness," the movie is racist. I'm not sure if this is a realistic argument or not. You don't watch movies to get educated about foreign cultures, you go for entertainment. I guess if you're enough of an idiot that watches a movie and thinks it's the gospel truth, then you're going to live in your ignorant bliss no matter what.
This commentary from NPR also presents an interesting view from a Japanese American perspective, pointing out how if you know Japanese and watch the film, it's quite different.