Arnold raced out of the door, and started...
In its time, it was once reported, this was one of the most often-read lines of fiction in the English language: it is the sentence fragment shown in a brief close-up shot of mystery novelist Jessica Fletcher's typewriter in the opening credits of Murder, She Wrote from 1984 to 1991. You can see it here.
Even conceding that "door" can be used as a perfectly legitimate synonym for "doorway," this always bothered me. One may race out of a room, and one may race through a doorway, but I don't see how Arnold could have raced out of a door—unless perhaps he had been standing still in the middle of the doorway before suddenly "racing" out of it, which seems unlikely.
What's interesting is that "Arnold raced out the door" doesn't bother me as much without the of, perhaps because I'm subconsciously putting an implied through into the sentence: "Arnold raced out [through] the door." Even so, I was surprised and amused to see that, out of all the examples they could have chosen, Merriam-Webster illustrates its definition of out as a preposition with the phrase "ran out the door." (Were the writers of this definition Murder, She Wrote fans, I wonder?) This doesn't seem to leave much room for my interpretation.
How should the clause "Arnold raced out of the door" be evaluated? Is it ungrammatical, grammatical but poor form, or grammatical with no reservations?