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Well, my verdict is in and it wasn't close: Austin Powers is actually a good movie. A very good movie, and for a lot of reasons.
Foremost, there is a basic simple structure and the movie sticks to it. Frozen in 1967 and defrosted thirty years later to defeat his nemesis, Austin Powers is a fish out of water. The script wisely keeps Austin front and center the whole time and doesn't take detours. It also successfully uses this premise, Austin's acclimation to the modern world, as a prop for jokes, creating a sense of unity. The film's other prop is Austin's untamed libido, the spark for love and conflict with his sexy-but-stodgy partner, Vanessa Kensington. That's it, but it works. Modern comedies looking for a model could do worse.
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Also, notice that each of those jokes is a different kind as well as degree. Another scene illustrates this variety even better.
Austin and Vanessa have been captured by Dr. Evil and, in spy-vs-spy tradition, enjoy a last meal with the villain before being put to death. On the one hand the scene plays like the staple from Bond movies where the villain lays out his grandiose plan, but the kick is that Dr. Evil's son is at the table and the kid is hassling his father about how he should kill his enemies. The result is that the dynamic of the spy plot is constantly jilted by the familiar sight of a domestic dinner-table squabble. Another scene is equally effective using this contrast. There, Dr. Evil attempts to discuss evil business with the henchmen at headquarters, but the failed henchman he just sentenced to death is screaming in agony downstairs. The scene upstairs is played like a board room meeting in which Dr. Evil is trying to pitch a proposal, but the tone is constantly upended by the screams coming from downstairs. Both of these scenes are peppered with smaller jokes, but the attention to tone and the subtle subversion is effective.
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There are plenty of other jokes in Austin Powers, too, from the escalating proof of Austin's ownership of the Swedish Made Enlarger Pump, to the two "accidentally" censored nude romps whose choreography to the Blue Danube waltzes suggests an elegance belied only by the visual innuendo and ever incipient nudity. Don't forget about the plain jokes, from Mama Cass' death via ham sandwich to Mr. Bigglesworth, from Dr. Evil's rolling chair too, of course, Austin's groovy vocabulary.
All of these jokes are stitched along the central threads of the spy satire and Austin finding his place and love in the modern world. Unlike its sequels, the latter is handled pretty gently and the movie finds a genial tone between laughing at and with Austin. We don't laugh so much at him as at the incongruity of his expectations and reality. By the end, we're surprisingly happy for Austin as he decides to be a one woman guy for Vanessa.
In short, Austin Powers is a blast that fulfills the promise of the swinging opening where all London is swept up in the magnetic spy's irresistible mojo, all the way through to the Man of Mystery's little apology for liberty: "now we have freedom and responsibility, and that's groovy baby!"