This is one of those movies that is just immensely good fun. First of all, it has an excellent cast. Caine is wonderful as the world-weary London private eye adrift in Los Angeles. Michael Constantine, as the ex-con desperate to find his daughter, has never been better. Natalie is very good as the satin-clad femme fatale. And then there's the outstanding supporting cast. In a sense, this film is a tribute to character actors. Even the unappreciated Robert Ito shows up as the sinister Japanese butler.
But even given the cast, what really shines is the W. D. Richter's script. Especially our hero's brilliant analysis of the location of a house based on the angle of the sun and the shadows it casts, followed by his discovery that: "I wasn't even close. It was in Beverly Hills."
On the other hand, your favorite bit may be the Humphrey Bogart impersonator reciting the credits at the beginning of the film to the accompaniment of a lone trumpet (at least, that's how I remember it; actually, since the other reviewer and I seem to be the only people in the world who have actually seen this film, who's to argue?) It's a sad fact that Peeper has been dumped. It doesn't even appear on most filmographies of Michael Caine. It's not available on video in any form, and I have never seen it appear on television (maybe we can persuade The Mystery Channel to show it, if the tape hasn't disintegrated by now). So if there's a patron saint of forgotten films wandering around this site, why don't you see if you can nudge 20th Century Fox into releasing it. It deserves better.