How to tell if your "Great Gatsby" is a first edition

As reported by Bloomberg:

“The Great Gatsby is considered, in collecting terms, the No. 1 American novel to collect,” says the London-based rare book dealer Peter Harrington. “A lot of that has to do with the dust jacket—people just seem to desperately want it.”.. Harrington’s book is priced at £275,000 (about $360,000), placing it at the upper tier of a booming collectible market...

The first edition numbered 20,870 copies. The easiest way to determine if a book is from this print run—aside from just looking inside the cover—is by checking for errors that were eventually corrected... One telltale sign from the first printing is a mistake on the jacket itself. The protagonist’s name, Jay Gatsby, is spelled with a lower-case j, “and rather than reprint the whole thing, they literally had someone go over it with a rubber J stamp”...

And if you've lost the dust jacket (which, incidentally, "was slightly too large, making it prone to tear..." -

That very first issue also has least five typos inside. Rare book dealer Heather O’Donnell, in a primer on the Gatsby first edition market in Lapham’s Quarterly, writes that on page 205, “Meyer Wolfsheim’s secretary tells Nick Carraway she’s ‘sick in tired’ of young men trying to force their way into the office.” 

Related: In the story, Jay Gatsby worked as a janitor at St. Olaf.