The opening shot (of the New York Stock Exchange's trading floor) has the subtitle "1985," which might lead one to expect that at least the action in the first few scenes takes place in the year 1985. However, when Charlie Sheen is talking to his Nimrod broker buddy the Nimrod jokes that the day the Challenger exploded, Gekko was on the phone "selling NASA stock short." The Challenger exploded in January, 1986, not 1985. [An explanation for this: Wall Street, as conceived and filmed, was supposed to be set in 1987. However, near the end of 1986, The Ivan Boaesky insider-trading scandal hit, many rules were changed, and acknowledging those events would have undone much of the plotting of the movie. So the movie was shifted back in time to 1985 (before the scandals, and also before the Challenger disaster), thus creating this major goof].
Bud Fox's name was originally Joe Fox, but it was changed after it was discovered Joe Fox was a real stockbroker, who wouldn't give permission for his name to be used.