Game Breaker: The Golden Knife. Although it's prohibitively expensive to use to just mow down everything in your path, it's powerful enough to render any enemy - including Dracula - harmless.
Goddamned Bats: Oddly enough, the actual bats aren't much of a nuisance apart from blending in too well with dark backgrounds, but the eyeballs that home in on Simon and those little hopping blue slime creatures are more than happy to step up as the most annoying enemies in this installment.
Mis-blamed: The translation is not good, but see Infallible Babble. The infamous "graveyard duck" line often cited as "Blind Idiot" Translation is actually a literal translation of the original Japanese dialogue — the best guess as to what it actually means is that it's either obscure slang for a night patrolman, or a Konami in-joke involving putting ducks in every game.
Most Annoying Sound: By the end of the game, the beeping that accompanies dialogue is probably gonna be ingrained in your head in a bad way.
In the reverse of what would happen to the next game, the soundtrack to the NES version is widely considered a massive improvement over the original Famicom Disk System version, which is generally hated by fans due to the tinny, whiny instrumentation, and a distinctly lacklustre version of "Bloody Tears."
Some of the American versions of the music are even included as bonus tracks on the Japanese soundtrack release, one of the very very few times you'll see "NES" on a Japanese product.
Scrappy Mechanic: There is no way to speed up the text box marking the change from day to night and back. And you'll be seeing it a lot. Fortunately time stands still when you're indoors.
Snark Bait: Borders on this. People do seem to enjoy snarking over more than actually playing it.
That One Level: Dead River/Jam Wasteland. Not only does it end with That One Puzzle, but to get there you have to cross a river on a bunch of one block-wide platforms moving vertically. If your jump is the slightest bit off just once, you're dead. Worst of all, it can be easy to miss getting the Red Crystal required for That One Puzzle, since you had to remember that, depending on whether or not you're holding a specific item, you can be transported to two different areas by the same ferryman. Forget the Red Crystal and you'll have to backtrack.
That One Puzzle: The infamous puzzle where you have to stand in a certain spot with a certain item and wait for a tornado to come and carry you to the next area. There are hints to the solution in the game, but the sheer insanity of it definitely qualifies it as this.
Vindicated by History: Maybe not the game itself, which still tends to be regarded as the weakest of the NES trilogy, but the gameplay style it pioneered would ultimately displace that of the franchise's original style, with Symphony of the Night.