I saw this movie first when I was a kid, so I knew it was one of the most appropriate for my kids to see. Outside of a few relatively mild curse-words (d*amn, a$$, etc.) it was perfect. The message of saving the whales for the future of humanity is very positive, as is the comeraderie of the crew of the Enterprise and their willingness to sacrifice themselves for the greater good.
STAR TREK IV is a good movie, and is appropriate for preteens and up. Outside of some tense scenes, language is the only thing wrong with the movie. There are several "a*s"s, "s**t"s, and "d**n"s. Spock uses "hell" in almost every phrase when he thinks it is appropriate to curse on Earth "ex: They told us the hell to come back to Earth". A man flips another off.
WONDERFUL! Interesting, topical, humorous, multicultural, well-done. I would show this to any child above 8 years old and expect to have a good conversation when the film ended.