The English voice acting in this game is the most prominent aspect in this case.
The PS1 English voice work was initially flat out reviled but over the course of the 2000s became a popular case of So Bad, It's Good. (While fans frequently compare the english voice work in the PS1 and PSP versions over which version is better.) But during the late 2000s/early 2010s there are a small but increasing amount of fans who think the English voice work in the PS1 version is genuinely good and underrated.
The PSP English voice work has this in spades as well... Is the PSP version's voice acting genuinely good and an unfortunate victim of the Nostalgia Filter from fans of the PS1 version? Or did the PSP version try to take the game far too seriously? Or is it really not any better than the PS1 version as they sound too generic? (At least the PS1 version tried to sound a bit more European as just about everyone in the PSP version sounded too American.) It depends on what you felt about the voice work in the PS1 version or if you are a fan of Californian Anime English Dub VAs such as Yuri Lowenthal, Wendee Lee and Michelle Ruff.
The Game Breaker items. Some feel that having them in the game completely kills the enjoyment of the game. Others point out that they're fun to use, and that people who complain about them can simply choose not to use them.
The credit song "I am the Wind", some fans love the song, others hate it and think it doesn't fit the atmosphere of the game.
Azaghal, the strongest sword enemy in the game, who not only is hard to hit, but will probably hit you during his knockback animation, dealing high (about 60-80 when you first meet him) damage.
Valhalla Knights. Especially when you first encounter them in the Colosseum.
The Salomes. They fly around erratically, constantly put up shields whenever you try and attack normally, and sometimes when you don't, spam orbs, skulls, and CATS that do surprisingly high damage, and are just a pain in the backside. Your only hope half of the time is just to get out, fast! Oh yeah, if you do kill them, they turn into a cat and run until the room ends or they hit a wall. They can still do high damage in this form.
Guardians, who deal slightly less damage than Azaghal, but throw up a shield every time you hit them when they're not in an attack animation. And there's only attack where you can hit it without getting hit as well, but most of the time they're too busy spamming shockwave attacks to bother with it.
Difficulty Levels: Sort of. Luck (thief) mode and magician mode offer huge bonuses to luck or intelligence (respectively) at the cost of all of your other stats. Magician mode cannot be accessed unless you have a clear game file saved on your card, and both are unlocked by entering a cryptic series of characters for your name.
Disappointing Last Level: The second castle. The same background music plays in six different areas (see Ear Worm below), very little if any story happens here (save for the final two bosses), and the game suddenly goes from linear to having minimal sense of direction. Not to mention that you can snag some Game Breakers here on your first playthrough, given enough grinding for random drops.
Ear Worm: "The Final Toccata", the music for no less than six areas in the Reverse Castle.
Fridge Brilliance: Alucard's first appearance in Castlevania III: Dracula's Curse and later canon appearances give him dark hair, but in this game it's white. He had just reawakened after sealing himself in a crypt for 400 years, so it makes a lot of sense that he'd look extremely pale for his assault on Dracula's castle.
Fridge Logic: How well Richter does in his battle against Dracula in the prologue determines Alucard's starting stats. But how does this even make sense? Having a hard time means either Richter is weaker or Dracula is stronger; the former shouldn't have any effect, and a stronger Dracula would mean a stronger Alucard since they're of the same bloodline. This doesn't even make sense from a gameplay perspective since doing well against Dracula means an advanced player, in which case the game should give Alucard worse states to maintain the level of challenge in the game. (This is how Dragon Spirit: The New Legend handles the same issue: if you lose the prologue battle you play an easier version of the game)
Many, many examples: the Crissaegrim, the Runesword, the Shield Rod + Alucard Shield combo, the Ring of Varda (which can only be obtained after beating the game at least once), Richter's Hydro Storm, and so on.
The Mourneblade and Sword of Dawn. Hell, yeah!
The Beryl Circlet isn't a Game Breaker, but it is definitely when fighting against Galamoth, since it absorbs electrical attacks.
Even the lowly Iron Shield is used in conjunction with the Shield Rod on various Speedruns to make short work of bosses.
And the Iron Shield itself can render Alucard invincible for a few seconds when a projectile comes in contact with it.
Alucard can throw three holy waters at a time. When used properly, this can kill bosses in under 30 seconds.
The Masamune has a special attack which does 2.6x the sword's normal damage, has great range, attacks a large area, and leaves Alucard invincible for its duration. And it's possible to repeat the attack just before the previous one concludes for potentially infinite invincibility.
Gremlins leave many stationary fireballs around as they zigzag though rooms, breaking your momentum.
Imps can dodge attacks and stun Alucard for a long while. This is worse than it sounds, because while he's stunned, Alucard will keep rapidly using both attack buttons involuntarily. Had a [use] item equipped to either hand? Watch in horror as your entire supply of it is expended against your will.
Armored Fleamen will prove to be an annoyance at first due to their usual jumping being combined with an axe.
And of course, the ever-present Medusa Heads, which now have a golden variety that petrify on contact.
When playing in 99 Luck mode, Alucard can skip the conversation with Death and keep his equipment: this is thanks to the greatly lowered defense from the Luck Mode combined with the special knockback animation you get if you take half or more of your max HP in damage from a single hit, allowing you to take a hit from one of the Wargs' charge attacks and be sent flying through the room where you encounter Death. It seems that in the PSP version, you can do this simply by leaving the screen before the cutscene starts. You get the Shield Rod reasonably early in the first castle. This means you get to start owning bosses with the Alucard Shield combo early.
By using the Sword Brothers spell in Master Librarian's room to enable them to open the menu while within the Librarian's menu, the player can use a glitch that may quickly maximize Alucard's money by selling him gem rings you no longer have, with negative numbers doing funny things when not anticipated by programmers, ending up with 255 of them and then selling those. This was one of the very few bugs actually fixed in the PSP version, unfortunately.
The original PS1 version of the game has a weird glitch involving a room with Frozen Shades: if you use the wolf form to quickly dash through the room until you hit an underwater wall, avoid killing the first and last Frozen Shade, attack right when you hit the wall and when jump out of the water onto the Ferryman's boat while backdashing back to the Frozen Shade with your shield out, turn into a wolf in mid-air over it and fall on it, the game goes into slow motion until you change screens and all items in the area will respawn infinitely, allowing you to max out your HP and hearts by collecting the respective Max Ups positioned next to each other in another part of the area, along with being able to get additional copies of any other items found in the area. If it sounds too obscure and random to believe, see this.
Using the Faerie Card in a certain manner can cause corrupt save games and mess up the inventory. This isn't the good bad bug, it's the fact that using this with a very specific set of items placed in a certain order in the inventory, can cause the game to arbitrarily run the hex values of said items as assembly code, telling the game to go straight to the ending, the best one to boot. Demonstrated by speedrunner Cosmo in this video.
Guide Dang It: Finding the items to get into the mirror castle without a guide is easier said than done.
It Was His Sled: The Inverted Castle. Nothing in the game hints at its existence until you succeed in unlocking it—the game even tries to trick you into thinking that the normal Castle is all there is to see with the map completion percentage. Nowadays, very few players fall for it.
Most Annoying Sound: PSHWPSHWPSHWPSHWPSHWPSHW! Boy, that Tin Man's annoying, huh? Plus, its high defense, ability to match your speed, and the fact that it's pretty much always attacking make it a tough cookie to silence. But you fought hard, and you finally shut the thing up! ...And then you enter the massive room filled with them.
Granfalloon (or Legion) is a massive ball of screaming, faceless corpses that constantly drop off and attack you, making it a one-boss Zombie Apocalypse.
Beelzebub is a three-screen-tall rotting corpse strung on meathooks.
The confessional in the Royal Chapel. Instead of music, there's a somewhat eerie ambient track with what sounds like a neverending clockwork bang. There are two seats for Alucard to sit on, which will cause either the ghost of a priest or a woman to appear, depending on what side of the confession booth Alucard sits on. Either will either listen to you/tearfully confess to you or stab you after cackling, depending on the color of their clothes.
Player Punch: Dracula might have been specifically going for this in-universe. Think about the fight with the fake Trevor, Sypha and Grant in the Inverted Castle from Alucard's point of view: he is attacked by perfect copies of quite possibly the only real friends he's ever had, and forced to kill them. Damn.
Porting Disaster: The Japan-only Saturn port attempted to add some extras to the game by making Maria playable and adding two new areas. Unfortunately the novelty of the new features are quickly canceled out by the actual quality of the port itself: the game suffers from constant slowdown when the screen is filled with enemies, most of the graphical transparency effects are lost, and the game loads before and after entering the transition rooms between areas (you know, those rooms that were there to lessen the loading times in the first place). This is because the game was a direct port. The game is built on a 3D engine (only noticeable in a few places like the Final Boss), and the Saturn had trouble handling 3D games.
Sequel Displacement: After a fashion. SotN was basically the sixth "main" Castlevania game and was released ten years after the very first game, but this is the game that informed what the Castlevania name came to mean in the zeitgeist at large. The earlier games certainly weren't unpopular, but none of them hold a candle to SotN's influence on the series or even wider adventure-exploration genre.
So Bad, It's Good: The original voice acting had this going for it for quite a good chunk of the fans. IGA saw to this being averted in the PSP version. In an interview he admitted that though he may not know English even he could tell that the dub was horribly awkward.
Strawman Has a Point: Possessed Richter says that he wants to resurrect Dracula so he can fight him for all eternity, because Dracula only respawns every 100 years and Richter has already beaten him. While said under possession and certainly out-of-character for a guy who's not a Blood Knight, Richter raises an interesting point. What is his worth once he's fulfilled his purpose? At best he can train his heir to take on Dracula, but even then his son/daughter probably won't get to fight Dracula either. Once he's done his part, Richter essentially becomes worthless.
That One Boss: Beelzebub can be trouble. He hangs from the ceiling, and is hard to attack because of it. His attacks involve summoning flies that do around 60 damage when they hit you and are annoying to dodge while trying to attack him due to how many there are.
The game is known for not being very difficult, but watch out for places such as a optional corridor in the inverted Castle Corridor with a pair of Blue Venus Weeds shooting roses all over the place while being helped by powerful Nova Skeletons.
Vindicated by History: The game is even more popular now than it was in the Playstation's heyday, and it became a Greatest Hits title even then. It certainly helps that the game eschewed the 3D of most games in its era, meaning it's aged extremely well compared to its peers.
Visual Effects of Awesome: Alucard's sprites are some of the most iconic in the series, with a whopping thirty frames of running animation. His cape is beautifully animated, and a late-game cape item lets you change its color, too.
Woolseyism: The skeleton enemy chasing its head was unimaginatively named "Soccer Boy" in the original translation. The localization changed its name to "Yorick", going from a bland joke to a rather clever Shakespeare reference.