Accidental Marriage: Near the beginning of the game after the airplane crashes in the Southern Country. Corum is rescued by the natives, and forced to marry Cynthia, the princess of the island, and eventual party member.
The most obvious one is in New Queen Town when Corum has to fight Baseran alone. If the player loses to her (which is likely) Corum is thrown out of the castle (naked), and all the while the party will stand in front of the castle where the fight takes place, and not rejoin him, and blocking him from getting back into the castle to re-fight the boss.
However, this is easily avoidable by just reloading one's save after losing.
Another rather deadly bug is known by Japanese fans as the Shuffle Bug, which involves constantly using a healing item on any character with full HP until the game's graphics and area boundaries wig out. Improper use of the bug can cause your save file to be corrupted or the game to freeze... though it also glitches out shop data, allowing you to buy plot-important items and beat the game as soon as you start it if you know what you're doing.
For no good reason Corum and El's defense stat will get bugged near the end of the game, dropping their defense a bit. Not really game breaking per se, just annoying.
There is also a chance of this happening to Johnny.
Due to a bug, only Corum's magic can be used outside of battle at any time, even if you're trying to use someone else's magic.
Thanks to some sort of memory overflow, the credit roll is rendered unreadable.
Gasshole: Princess Gourmet's only real abillity is Farting. It makes you wonder why the townspeople was so scared of her.
Guide Dang It: Some treasure chests have secret compartments with other items inside, but to check this you'll need to check already open chests. To this troper's knowledge, however, you'll never find plot-important items this way, so unless you want to do a 100% completion run of this, you shouldn't worry too much.
Infinity+1 Sword: Well actually a dress in this case. Fairly early on in the game the player can purchase the Powered Dress (armor) for El, immediately making her the strongest character due to its bugged stats.
And to make matters worse, there is a Powered Dress II, that can be purchased late in the game, but for a very high price.
Mirror World: The Past Life World visited late in the game. The Past Life World seems to be more of a conglomeration of the different time periods from the main cast's past lives, than one point in the past.
Thankfully, at least on the Overworld Map, they can be avoided by using the Kattobi Rocket, given to the party fairly early on by Dr. Pascal, to warp between already visited towns.
The Harite item also helps, by allowing the party to fly, but it's only usable for a short span of the game.
Although it can only move over water...
But hey, it has a great song that plays when piloting it.
Reincarnation: All of the main characters are reincarnations of great heroes from the past, and are able to transform into their past selves to perform special abilities (which serves as the game's magic system).
Johnny and Cynthia were lovers in their past lives also
Spiritual Successor: The creator of the game, Office Koukan, actually made another RPG after this known as Idea No Hi, or Day Of The Idea. It's got an oddball sense of humor similar to Maka Maka's, but a more serious story, fairly interesting gameplay mechanics, and actual bug-testing to its name.
On a related note, after defeating Ramonu, the player must use the magical gender changing fountain to change the male party members into girls, in order to sneak into a Women's Bathhouse to get a key.