Bribing Your Way to Victory: SQEX Coins, which can be used to buy consumable(!) items needed for certain sidequests. Duh. Also can be used in the Ultimate Job System to buy more (and better) tickets.
Disc One Nuke: The Samurai, which has enough attack that pretty much all of the lowest tier characters will be decimated by it in the arena, particularly if leveled. Silver cards (except magic ones), which are available if rare to even first-time players, help keep this in check as time goes on, but see below.
Fantasy Character Classes: Novice, Fighter, Healer, Monk, Machinist, Paladin, Thief, Dark Knight, Conjurer, Samurai, Chaos Lord, Gunner and the Halloween-special Witch. More classes are added every now and then. As of the introduction of the new job system, the classes became job cards that need to be merged to gain levels.
Fusion Dance: Two forms - one, Ability Merge, allows you to take the arena abilities from one card and give them to another (which destroys the cardtaken from). The other is Special Merge, in which two particular maxed-out cards merge permanently into a brand new card at level 1, with abilities taken from the base cards.
Gotta Catch 'Em All: The only way to obtain more character classes is to complete the collections of whatever MacGuffin the game throws at you (keys, orbs, scrolls, bullets etc.).
Changed to a different form of the same as of the "Ultimate Job System" update - now jobs are divided into one of five levels (Normal, Bronze, Silver, Gold, Ultimate), and you get tickets (one free per day, more from quests and battles) to spin a randomizer to get more. Of course, you're not going to get all the jobs unless you collect those tickets. The old form exists still, but with the collections merely giving more items for Player Vs Player battles.
Luck-Based Mission: Which jobs you get as of the Ultimate Job System update are either from Randomly Drops in quests (which only get you the two lowest levels of cards, and never the best version of same) or from spending tickets which can get you any card from one of three categories.
I Am Who?: You're actually a descendant of the Arcani, who are the titular Knights of the Crystal. So is Stein.
Purely Aesthetic Gender: Before the changes of the class system, one could change the gender of their character's sprite as much as they liked.
Still mostly true after the update - while the genders do have different stats, the difference is generally minor except for some of the gold and ultimate cards at high levels. There are a few classes (the samurai-based classes and the classes that affect quest completion percentage) that avert this, however.
Quad Damage: Most of the offensive abilities in the arena, although they generally only give a percentage boost. Petrify effects, however, give a straight multiplier. Inverted by the defensive abilities, which similarly provide a percentage boost to the various defensive stats.
So Last Season: New jobs that get introduced are generally balanced against what already exists for use in quests and battles (for example, the explosioner, when introduced, had the same effect as the cardinal of the same quality and level), but they're generally noticably more powerful for arena use (even before accounting for the Tactical Rock-Paper-Scissors, said explosioner will have about 40% higher stats than the cardinal). They've now introduced non-merged silver cards with stats comparable to early non-merged gold cards.
Tactical Rock-Paper-Scissors: In the Arena, jobs are classified into three types: Weapon, Bare Hand, and Magic. Weapon-based jobs beat Magic-based jobs, Bare Hand-based jobs beat Weapon-based jobs, and Magic-based jobs beat Bare Hand-based jobs. There are exceptions, though: the rules of this combat triangle may be subverted when the job level is high enough, arena ability(ies) are activated, or both.
With the quest update that brought along the Moon World, Wonderland, and Titan's Tower areas, the bosses of these areas fall into this, being vulnerable respectively to Smash, Heal, and Magic characters.
Turns Red: All the bosses do this after you reduce their HP to 50%. This increases their attack speed and attack power to incredible levels, turning the fights into Luck Based Missions. Your only chance is to hope that your party members can fire off their special attacks before they get KOed.