1.

This is probably a bug.

When you're on the deck of the salvage ship, you can talk to the top-left Al Bhed and he'll give you x3 potions. If you dive, go into the next room, return, then climb back aboard he'll be reset and give you another x3 potions. Rinse-repeat. Not that you'd want to.

2.

The beginning monsters in Zankarand don't ever hit you. You can obtain Warrior, Slayer, and with a bit more persistence, Solo and Daredevil, over-drive modes by continually hitting the rear monsters. I got Warrior and Slayer (Slayer is VERY GOOD for the early stages and gives Tidus a fighting oppertunity to obtain all his overdrives early), in exactly 1:00 hours on the savepoint after beating the sinspawn boss. Auron will get his modes first, as it seems overkilling a monster speeds up the process. I obtained slice-and-dice from fighting underwater fishes with Rikku in less than two hours play-time.

Unfortunately, you get absolutely zero in the way of gold or AP from doing this.

3.

I have not tried this one yet, it's something I'm saving up (though I know that it works in principle). Optionally, and perhaps necessarily, you will want to have all, or at least the party members you're interested in, reach Kimhari's starting position on the sphere grid (I haven't checked the default sphere grid, but on advanced, Kimhari is pretty much in the center, encircled by everyone else's starting positions, and noone is more than about 10 moves away from his position), then learn lancet.

If you are VERY tenacious, you can then move into Tidus' section and obtain "haste" for all your characters. I'm not sure just how feasable this is from killing Besaid monsters. But it will make the next part all that more "fun".

When you board the ship and reach the Sin battle, there is an infinite supply of Sinscales, worth 2 or 3 AP depending on whether you overkill them. When each three are slain the battle is intercut with an annoying animation showing Sin launch more Sinscales. Not to mention the fact that when Sin gets his turn in battle it just shows another animation. This can slow the process down, and it's one reason why haste is desirable to cut down the number of turns Sin gets, thus cutting the tedium.

The lancet power is used on fresh monsters to replenish both your HP and SP. Without lancet, the time you can endure this battle is limited, and it would be a darn shame to die in the water to that second boss after you decide to stop.

Using this process, you can get overddrive modes for all characters, and a heap of AP and gold for that stage of the game. For contrast, if you focus only on beating Sin's fin, you'll get a mere 22 AP from this battle and the next one.