Games

There are prolific glitchhunters in the speedrunning community that have a knack for finding useful bugs, so it's definitely a skill. For things like finding seams in level geometry, it's probably more or less as you described (perhaps with some finesse to it). And with any game, simply playing it enough will inevitably uncover bugs, especially early in development. But on a broader scale, I think the core is identifying the game's invariants (fancy term for "things that are assumed to always be true") and figuring out how to violate them.

For instance, take the classic Trainer-Fly glitch (a.k.a. Mew glitch) in Pokémon Red & Blue. In this case, the invariant is, "Once a player is spotted by a trainer, they will inevitably scroll through their dialogue and then enter a battle with that trainer." This is something the game does not explicitly check for, since it assumes that the other systems in place will ensure that it is always true. By exploiting long-range trainers, the fact that trainers are drawn facing down the first frame they are drawn on screen, and the fact that pausing interrupts gameplay and allows you to leave the map after you are spotted via fly/dig/escape rope, you break the invariant. At this point, the game is in a state with undefined behavior, which is where the fun begins. In general, that kind of state transition (walking around freely → being spotted by trainer) is a fruitful place to find glitches, since both states will have different sets of assumptions and the handover can be a complex affair.