Anvilicious: "Grow up and stop being Bastards or someone out there will make you stop." This is a damned good one. They way Klaatu delivers the message at the end, the audience is made to feel as if he is talking directly to them. Especially poigniant when you remember that this film was released during the height of the Cold War.
Director Robert Wise later said that while most of the Christ allegories were intentional, the use of the name "Carpenter" was a coincidence that he never noticed until it was pointed out to him years later.
There's a scene where two doctors are discussing Klaatu's physiology, and one mentions that Klaatu supposedly has a life expectancy about twice that of a human. As they speculate about what medical advances might be responsible for this, one of them produces a pack of cigarettes, and they both light up.
There's also a scene in which a news bulletin is heard talking about Klaatu, in which the announcer speculates the two most likely candidates for his homeworld are either Mars and Venus because those are the only two planets capable of supporting life... we now know that Venus is most definitely not capable of supporting anything what with the runaway greenhouse effect that makes it hot enough to melt lead, and none of the many probes we have sent to Mars have ever produced solid proof of any kind of life, let alone something intelligent enough to develop interplanetary travel, despite very thorough searching and more clear maps of the planet than we have of Earth.
Klaatu's chosen alias John Carpenter. It also counts as a case of pure serendipity; see "Everyone Is Jesus In Purgatory" above.
Narm Charm: Gort visibly creases at the knees when he walks, rather spoiling the illusion of an all powerful robot, but the film is good enough that you just don't care.
Special Effects Failure: Gort visibly creases at the knees when he walks, rather spoiling the illusion of an all powerful robot.
Also note the obvious wires holding Helen up when Gort is "carrying" her (the actor playing Gort was tall but not very strong, and simply couldn't carry her on his own).
Strawman Has a Point: The humans are lambasted for "striking first", but the craft landed with little warning in a capital city, Klaatu walks directly at the humans with an object held up that snaps open unexpectedly within melee range — and didn't expect humans to flinch?
In a greater scope, humanity in general. Klaatu arrives with zero warning, shuts down all power on Earth (with the exception of hospitals and in-flight airplanes), which potentially caused thousands of deaths, all to deliver a message of complete annihilation if they do anything remotely "threatening" to a planet they didn't even know existed (and mentioned above, still don't) solely because Earth has the theoretical capability to attack them, not because of any action Earth intentionally or unintentionally made against them. This makes Klaatu's planet look extremely hostile and xenophobic, ruining the film's intended message.
The hospitals and airplanes business is to indicate not only is Klaatu capable of shutting down technology but he can do so on a microscopically specific level across the globe. As such, almost certainly no one was killed.
They Wasted a Perfectly Good Plot: Unfortunately the film loses the Wham Line from the end of the original short story, where the protagonist fearfully begged Gnut (Gort) to relay to his masters that what happened with Klaatu was an accident and the people of Earth meant them no malice.