The thing that most of us mean when we say it's broken is that the junction system is so easily exploited to make your characters really powerful that there ends up being no challenge to the game.
It's very easy to get fairly high level magics early on by quickly teaching GF's the refinement abilities. Even just teaching them mid magic refinement and later high magic refinement, or whatever it was called in the game makes it easy, if somewhat cumbersome, to get more powerful magic than you should have and start junctioning it to your stats to up your HP, attack, and everything else.
The example I always use is that once you gain the ability to refine healing magics from items, Curaga becomes absurdly easy to get since you can refine it easily from tents.
Basically, if you want to make your characters more powerful, the key is to learn the refinement abilities and status junctions as early as possible, and draw from enemies while keeping an eye on what new items can be refined to make, and where you find them. Even without a lot of experience with the game you can make your characters strong enough that you'll probably never die.