One night, napping in his chair, he is awakened by a scream. Later that night, he sees one of his neighbors, Lars Thorwald (Raymond Burr), repeatedly leaving the apartment with a huge, heavy suitcase and returning with the same suitcase significantly lighter. Put that together with Thorwald cleaning off a large butcher's knife, the apparent disappearance of his nagging wife, and a number of other "suspicious" clues, and the audience, like Jeff, has no doubt that Thorwald has committed foul play. Nonetheless, even at the end, and this isn't much of a spoiler for you Rear Window virgins, Hitchcock chooses to present our "proof" of Thorwald's guilt in a far more circumstantial and vague manner than he might have. Could Jeff (and the rest of us) still be wrong?
Rear Window was nearly perfect when it was released, and it still is. A very few minor elements have dated: Modern audiences chuckle when a huge deal is made over whether or not Lisa is spending the night, as though it would be scandalous in 1954 for two sophisticated New York adults to sleep together without the benefit of wedlock. On some level, though, that social anachronism works in the movie's favor: Hitchcock was a master at cranking up eroticism through discretion. And there are few moments in the history of film as romantic or as sheerly sexy as Stewart and Kelly's first kiss.
Nearly Perfect: Thelma Ritter, Grace Kelly, and James Stewart in Rear Window.
The possible thematic readings of Rear Window are no less complex or resonant than those of Vertigo: Jeff is akin to a film viewer who finally sees the security of his one-way perspective collapse as the creature on the screen comes lumbering down into the auditorium to get him; Jeff, terrified of emotional entanglements, is using his involvement with the courtyard denizens as an excuse to ignore the very real, willing, and infinitely more alluring Lisa; Jeff is morally reprehensible, even if Thorwald is guilty; and, most broadly, Rear Window is a metaphor for how we all assemble our worldviews from fragments of perception that are often (if not always) unclear and decontextualized.
There are lots of other ways of looking at Rear Window -- all of which you can ignore if you want, because there is no other movie currently playing in theaters that is more satisfying simply as a romp. It has the thematic content of a Bergman film (profound and richly ambiguous) perfectly integrated with the light, luminous surface of Lubitsch (funny, sexy, scary, and exciting). What more do you want?