This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
Big Joe might be sort of a joke character in the game, but he actually
does have some secrets. Here's where to find them:
1. Nortune: Once Fei becomes the battling champion, and you can access
the A Block of Nortune, you can see Big Joe standing near an alleyway in
the town. Joe will ask for some money (something like 10,000 G) in
exchange for "something special". Give him the money, and he'll take it
and run. Later on, after the raid on Nortune, return to the same
alleyway to find an M Disc, which you can use in the A Block bar to play
plenty of music. (Joe will also reappear next to the town exit with some
"muchacho information" for you.)
2. The Thames: After the Yggdrasil arrives in Thames, walk to the front
of its top deck and you'll see Big Joe. Talk to him, and you'll play the
familiar Thames card game. If you win, you get the LongDarkCoat, a
useful defensive item.
3. The Ethos HQ: After the Ethos is attacked by Gebler, before taking
the elevator to the basement, search the area around where Fei was
hospitalized. Somewhere around there are some jail cells. Take a peek
into all of them. Hey, look who you saved!
4. Shevat: Big Joe can be seen doing absolutely nothing below one of the
staircases inside the maintenance area of Shevat. How'd he get there?
5. The Lighthouse: Inside one of the open shops in the deserted town is
Big Joe's Gear Shop. It has some incredibly powerful equipment for
gears, but it's very expensive. Still, this is the place where you'll
find a 100-output engine and perfect armor.
6. The Lighthouse: Also inside the lighthouse, there's another shop
which looks like a convenience store. Browse through the store to find
documents explaining infinite attack power and secrets about the
Eldrige. Keep reading the Eldrige secret over and over again, and you
might find a document telling you the shocking story of Big Joe. Then
again, you may not want to read this...!