Find the theme of the movie. If you can't discern the message the movie is trying to convey, try describing the movie to someone else. You tend to talk about what struck you the strongest, usually the theme. Be aware that smaller themes can also be contained in a movie in support of the larger theme.
Look at the storyline. Analyze whether the plot flows easily from one scene to another. Note if the screenwriters followed a well-used formula from the hero cycle or added twists that make the plot more believable and draw the audience into the story.
Listen to the dialogue to analyze if it's believable or contrived. Forced explanations should not be sprinkled into the characters' conversations to explain the story to the audience.
Look at the set and scenery used for the movie. The atmosphere of the film is often enhanced with the use of lighting, special effects, costumes and backgrounds. These elements of the film should work together to bring the audience into the story but shouldn't overwhelm our senses and detract our attention.
Consider the roles of the main and supporting characters. It's not always the heroes that draw us into a story but the damsel in distress or villain who plays a role that makes the film memorable. Stereotypical characters are often the easiest to spot; however, their role is usually of little importance to the theme.
Watch for scenes that do not add to the story and should have been edited out. Editing a movie is an art, and needless pieces should be left on the cutting room floor. Also when analyzing editing, keep your eye out for the way the scenes move from one to another; the audience shouldn't lose track of the story because the movie jumped around from scene to scene.
Watch for symbolism, used to represent some topic or idea from the theme. This could be a repeated object that the camera focuses on throughout many scenes, or a word or phrase that is repeated. Be careful not to find symbolism everywhere, an easy thing to do if you're looking to make meaning where none is intended by the director.