Catherine Martell's first name is spelled as "Katherine" in this episode's opening credits, but as "Catherine" in all other episodes.
Bobby and Mike leave the sheriff's station during twilight. In the next scenes (taking place the same day) it's completely light (and sunny) outside.
Near the end of the episode, the sheriff turns on the siren and flashing light when chasing James and Donna on a motorcycle. In the following shot, the siren and light are off.
Joey Paulsen takes Donna out of the Roadhouse brawl to go meet James, driving away and being followed by Agent Cooper and Sheriff Truman. When a shot establishes the bar brawl is continuing, Joey and Donna are seen sneaking out past the bartender again.
At no point during the pilot (e.g. when the Sheriff and doctor first inspect Laura's body, or later, when Cooper examines her), do any of them ever wear gloves. That has been a standard forensic practice since early in the 20th century, and certainly, not a practice that an FBI agent would be likely to violate.
The Norwegian delegation uses an interpreter. Like most educated Norwegians, all international businessmen in Norway are fully fluent in English. They never use interpreters.
When James and Donna decide to bury James' part of the necklace, there is already a hole waiting for them.
When the police car passes Bobby and Shelly in their car, the siren correctly changes its frequency because of the doppler effect. However, at closer listening this is revealed to be an inferior sound effect: First, the siren's frequency doesn't get elevated (the sound doesn't get higher) during approach, and second although it sounds lower when receding, its frequency not only stays the same, but the alternation between high and low beeps gets slower, revealing it to be a slowed down recording to achieve the effect. An approaching or receding sound isn't perceived faster or slower, it just changes its frequency from the listener's point corresponding to the distance.
While Ben is pitching the Norwegians, the hotel secretary enters to inform Leland that his wife is calling. The secretary mistakenly calls Leland "Ben."
As Sheriff Truman picks up the phone to take the call about Laura's body from Pete Martell, the reflection of the director wearing headphones can be seen in the glass.
Laura Palmer's body is found on what is supposedly a lake shore in front of the Packard home. During the filming sequence however, the tide lowers and the shore becomes more exposed - a highly unlikely occurrence on a lake. The scene was filmed at the Kiana Lodge on Agate Pass in Puget Sound and between takes, the tide went out.
When Cooper examines Laura's body for the first time, he turns to a doctor and asks him to leave him and the sheriff alone with the body. The actor, mishearing the line, replies "Jim" - his name. Cooper pauses for a moment and repeats the question and the actor apologizes and leaves. According to commentary on the 2007 DVD release, this was a genuine blooper but director David Lynch liked the surreal moment and kept it in the finished product. According to the same commentary, the flickering fluorescent lights were genuinely malfunctioning but Lynch felt it helped the scene so chose not to replace the lighting.
In the closing credits, actress Kimmy Robertson is credited for playing the role of Lucy Morgan. The door to the character's office has a name plate which clearly says Lucy Moran.
Not long after the class scene where Donna starts to cry and James breaks his pencil when they have a premonition about Laura Palmer being dead, Principal Wolchezk makes an announcement. With the previous scene in mind, he tells about Laura Palmer as their classmate, whilst actually the announcement is meant for the whole school.