In my second game as Keeper I did a cruel thing to Jenny Barnes. I used a mythos card on her that said that her gun was out of ammo and that she had to discard her weapong. I interpreted this as she was forced to return her guns to the box but later started thinking. In all the other cases I have seen the cards says to drop the weapon not discard. And one of the actions an investigator can do is to discard items and by doing so drop them in the room.

So the question is, in the case of the mythos card with the out of ammo text, should the gun be dropped in the current room or should it be discarded and returned to the box?

Hmm... I always just read discard as 'out of play' and never had anyone question it.

Pro's for having it mean drop: It is a total screwing to take a character or set of stats that are lower to get a weapon and lose it on turn 1. (I've seen this happen multiple times).

Con's for it meaning drop: I don't get why I'd drop a gun becuase it was empty if I had the means to reload it! Why could someone else pick it up and use it then if it had no bullets? What does this mean when played on an Axe or a Typewriter?

As usual, I don't have my cards/rules in front of me. If the action an investigator takes to drop items is called 'discarding' then thats a strong point.

"Drop" and "discard" are two different things. The Drop action does not say anything about the investigator discarding items. They are quite separate.