Anti-Climax Boss: All of the bosses, once the player has completed all of the missions. They come without reinforcements despite not being especially strong in any way - thus, the final mission of each level is just to kill three random enemies as they come.
That One Sidequest: Kill Frenzies, the equivalent of rampages in later games, in the PC version. They aren't particularly hard in the first district, but become one of the hardest challenges in the whole GTA franchise once you reach the second district. They start requiring killing cops or destroying cop cars instead of civilians or regular vehicles, which not only is more dangerous, but also more annoying since usually there aren't enough cops chasing you (and therefore you'll run out of time). Besides, there's a notable Game-Breaking Bug which corrupts your savegame after completing a Kill Frenzy activated by entering a vehicle initially place on a trailer. The only known player who has proved to have completed all them did so through different exploit and glitches.
What an Idiot: Incredible stupidity among non-playable characters is incredibly rampant, whether by design or by programming limitations or both. Even aside from flat-out cases of Too Dumb to Live, there are forms of stupidity not directly lethal to oneself, such as police officers whose response to you indefinitely blocking their vehicle is to... just honk at you. Repeatedly. But nothing more, no matter how long you're blocking their vehicle for.