"Anchors Aweigh" is the product of the classic MGM musical production unit, and on the whole the film is every enjoyable good music by Jule Styne and others, excellent dancing by Gene Kelly (and even a passable job by Frank Sinatra), and a funny well-paced script. The only major element I would criticize would be the casting of Kathryn Grayson, whose presence in a film always means the audience will be subjected to endless pseudo-operatic warbling from the petite Miss.
Kelly plays a naval serviceman named Joseph Brady, a man with a mythic reputation around the ship as a lover but whose Valentino-charms are constantly being subdued by the presence of his less cocksure friend with the improbable middle-American name of Clarence (Sinatra). Upon receiving 3 days of shore leave for saving Clarence's life, Joe reluctantly agrees to help Clarence find a girl based on the dubious premise that he owes him something for saving his life. They are drafted by a policeman (Rags Ragland), who needs them to help coax a precocious young boy (Dean Stockwell) who wants to join the Navy into returning home to "Aunt Susan" (Grayson). At first it is Clarence who is interested in wooing "Aunt Susan" but eventually Kelly's character emerges as the more likely candidate.
There are several standout musical scenes but nothing to come close to Kelly's more famous work in films like "Singin' in the Rain" and "American in Paris". The closest we get is a gimmicky sequence with Kelly's character in a fantasy sequence dancing with Jerry, the mouse from "Tom and Jerry" (although he seems to be closer in size to a dog or cat here than to a mouse). It's a startling sequence for its time but doesn't have enough complexity or emotion to really stand the test of time. I actually enjoyed the parts of the sequence that took place prior to the animation, where Kelly was using semi-balletic moves to emphasize the transition into the fantasy world and where we see him dance down a tunnel that looks like something right out of "Alice in Wonderland".
Eventually the characters find their way to Susan's favorite bar, a somewhat sanitized Mexican restaurant/bar in Tijuana. There the patrons happily allow Ms. Grayson to chirp her arias with abandon, and the management becomes very excited at the opportunity that Clarence and Joe have extended for her to sing with their "friend" Jose Iturbi (playing himself with a light humorous touch). Of course they've never met their "friend" Iturbi and they spend much of the film's length trying to reach him (in an amusing scene Sinatra's character meets Iturbi but mistakes him for a piano tuner and urges him to abandon tuning pianos and try a professional career), sneaking into the studio and the Hollywood Bowl, where Iturbi is rehearsing a surreal symphony comprised of dozens of young piano players you haven't seen anything like this outside of "1000 Fingers of Dr. T". Iturbi himself is a kind of a god-figure in the story he represents the opportunity for salvation from the drudgery of unfulfilling work and the possibility for fame and artistic achievement for the heroine. Everyone is 100% sure that as soon as Mr. Iturbi so much as hears Ms. Grayson, her operatic career will be a reality. The 3 primary characters are desperate to reach him and they think of him as some kind of remote and distant mythological figure a lot of the film's charm and humor comes from the contrast of this perception to the very down-to-earth "real" mannerisms of the maestro. And speaking of Iturbi's contributions to the film, he also provides a very stimulating musical moment with his orchestral interpretation of "Donkey Serenade".
When all is said and done, this is a film that nobody who enjoys musicals will want to miss. The majority of the music was written for this film, a nice contrast to recycled soundtracks for other Kelly opuses like "Rain" and "American". Kelly is still at his early peak, adventurous and boisterous in both his dances and his interpretation of the character. Sinatra's voice was never in better form and he rarely had better songs to sing. Stockwell is a charming addition to the clan, and Grayson's character is endearing when she isn't posturing on stage. Iturbi adds that well-grounded but sophisticated tone that perfectly matches the atmosphere and style of the classic-era MGM musical. This is one of the better ones.