Was the author's use of the word "accidental" on page 162 to describe Gatsby the correct word to use? "There was a faint, barely perceptible movement of the water as the fresh flow from one end urged its way toward the drain at the other. With little ripples that were hardly the shadows of waves, the laden mattress moved irregularly down the pool. A small gust of wind that scarcely corrugated the surface was enough to disturb its accidental burden. The touch of a cluster of leaves revolved it slowly, tracing, like the leg of transit, a thin red circle in the water."

In the full text version of The Great Gatsby that I consulted, the quotation reads slightly differently, as per the portion I have italicized:

A small gust of wind that scarcely corrugated the surface was enough to disturb its accidental course with its accidental burden.

There are two ways to approach answering this question. One of them involves the author’s intent, and the other relates to the reader’s interpretation of Gatsby’s death and demise. Each reader might decide that the two aspects coincide, overlap somewhat, or are completely different.
“Accidental” in the longer quote is used to describe both the movement and the placement of Gatsby’s body on the air mattress in the pool. As the sentence follows one saying that the mattress’s movement was irregular, “accidental” could be a synonym for “irregular.” F. Scott Fitzgerald may be implying that the mattress had come to rest upon the water by accident rather than design, or that a swimming pool is not supposed to support a dead body. Because we learn later that Wilson shot Gatsby, the second interpretation is more likely to be consistent with the author’s intent.
In terms of a reader’s interpretation of Gatsby’s murder as a fitting ending to the novel, the “correctness” of the word would largely correspond to the way each reader views Gatsby’s life. Because Fitzgerald uses Nick to tell the story, we are presented with a biased view. Nick’s affection for Gatsby, painting him as a romantic hero, puts a more positive spin on him and seems to disregard his illegal businesses. As Gatsby was not in fact Myrtle’s killer, Nick may be implying that he was an innocent victim. A reader might judge Gatsby more harshly, and conclude that—even though Wilson shot the wrong man—Gatsby’s criminal activities were likely to bring him to a bad end.
http://gutenberg.net.au/ebooks02/0200041.txt

Yes, "accidental" is the correct word to use in this sentence. This passage describes Gatsby's dead body lying on a flotation device in the pool. Nick describes a scene that is strangely serene, in contrast to the misery and suffering that just occurred when Wilson shot Gatsby. The only force that disturbs the scene is a slight wind that blows across the surface of the pool, causing it to ripple slightly. The "accidental burden" on the surface of the pool is the "laden mattress," or the flotation device on which Gatsby's inert, dead body lies. The word "accidental" could have different meanings in this context. It refers to the idea that Gatsby was killed in an accident, and it also refers to the idea that his body should not be lying inert in the water. It is only by accident that Gatsby's body has become a burden on the surface of the pool.

It's important to remember that the full line is as follows:

"A small gust of wind that scarcely corrugated the surface was enough to disturb its accidental course with its accidental burden."

So Fitzgerald uses the word twice in the passage to which you refer. Gatsby's body is an accidental burden in that it doesn't belong on the mattress; it could just as easily not be there. The breeze would still blow; the water would still gently ripple, though not quite in the same way. But Gatsby's body provides an "accidental burden," an additional object upon which the forces of nature must work.
The burden of Gatsby's body floating on the mattress diverts the water from its natural course. In that sense, the water's course, like the burden of Gatsby's body, has now become accidental, in the sense of something that isn't intrinsic to the nature of a person or thing. The water's substance, and the way it is normally expressed in its gentle, unimpeded flow, has been disturbed by this sudden intrusion into its natural rhythms. 

I can understand why one could argue the word is incorrect, but I would say that the use is correct. The "accidental" burden is Gatsby himself. Admittedly, Gatsby is not on the pool mattress, or float, as we would call it today, by accident. Gatsby, who had not once been in his pool all summer, very intentionally decided to make one use of it before it was drained for the season. The "accident," of course, is that he is on the mattress dead. He had no idea when he began floating around the pool that this would become his deathbed. In fact, he is killed by accident, by mistake. George Wilson believes Gatsby ran over his wife, Myrtle, and then coldly drove off without even stopping to see what had happened. However, unbeknownst to George, Daisy was the person driving the car. As a result, one could say the "burden" of the dead body on the pool mattress is accidental.