All experience goes back down to zero when you get lose all your lives and get a Game Over. 20 EXP away from a level up? Too bad, it's all a waste, should have gone to an easier area to grind that last bit. And those big EXP pick-ups you grabbed during this time? Oh, they're not coming back. And this isn't even taking into consideration the large number of enemies who steal EXP whenever they hit you. They can't drain levels from you, but if you've collected 200 EXP and are 100 away from a level, getting hit enough will force you down to 0/300 EXP to the next level. Basically, in order to level up efficiently, you have to make sure you're not anywhere near EXP drainers (and they're annoyingly common).
Oracle Of Ages added a wonderful mechanic for the Mermaid Suit. You have to constantly tap the D-Pad in the direction you want to swim in, not hold the D-Pad as usual. This makes the sixth and seventh level bosses extremely annoying, thanks to both fights being fought underwater (the sixth boss is both under and above water).
Made even worse in their Virtual Console release on the 3DS. You either had to double tap the circle pad (which is as inefficient and potentially inaccurate as it sounds) or, on an original 3DS at least, an incredibly stiff D-Pad.
Having to pause and go to the equipment screen to change between normal shoes and iron boots over and over and over in The Legend of Zelda: Ocarina of Time's Water Temple, where you need to walk on the bottom in some places and float in others to complete it. (Thankfully, the remake and next games have the Iron Boots as an item you can equip to one button for easy switching.)
Made worse by the fact that it takes ages to switch to the pause screen, as every time the player presses the Start button, the game slowly generates a screenshot of the game in order to use it as the background for the pause screen, not showing this one until the process is finished.
When you travel back to the First Day in The Legend of Zelda: Majora's Mask, you lose the ammunition of your items, meaning that you'll have to collect bombs and arrows again when going to a dungeon.
Kinstones in The Legend of Zelda: The Minish Cap, for wasting one of the GBA's precious four buttons on a seldom-used function. And the people you fuse Kinstones with keep changing. You could attempt to fuse Kinstones with somebody, discover you don't have the right type, and come back later when you do to discover that that particular fusion has moved to someone else. It's particularly bad when there are certain fusions that will always be from a specific NPC, but they won't always be willing to fuse Kinstones with you.
Some possible Kinstone fusions will be Lost Forever if you don't fuse them at the time the game wants you to fuse them. It's especially annoying when at one point in the game, Tingle will fuse Kinstones with you, but come back later in the postgame with only one Kinstone left to fuse and he suddenly won't want to fuse with you.
Wind Waker's sailing deserves special mention here; while it's essentially the same mechanic as Epona the horse, at least Hyrule Field has more visual diversity. Epona also didn't require you to play a song every time you wanted to change directions for max speed, and the Great Sea is much larger than Hyrule Field. Of course, a Broken Base has developed around this mechanic, as about as many fans who hated the mechanic also loved it. Slightly changed in the Updated Re-release with the edition of a "Fast Sail" that doubles your speed and eliminates the need to manually change the direction of the wind, of course the issue of whether it's needed or it ruins the experience of the game leads back to the same argument.
You found a silver rupee! That's worth a whopping 200 rupees... but your wallet is full, so let's put it back for now. Some may find it better than the alternative used in previous games where any found rupee would be erased if you tried collecting it with a full wallet, but they may think otherwise while searching for the last "unopened" chest in a dungeon.
There's also the annoyance of the game having to give you a description of higher valued rupees the first time each time you start up the game, even if you found them on the ground.
The train travel is this, mainly for three reasons: One, because of it, overworld travel is on rails, literally. Meaning that you can't freely roam and explore it. Two, if you happen to die (which is gonna be the case quite frequently, given the number of attacking monsters and evil trains in the open fields) you reset to the location you started. Three, somebody thought that it would be funny to complicate the fairly simple teleport mechanics from the previous games down to the point where they are barely of any use anymore.
Another despised aspect of Spirit Tracks are the Pirates. They are far more frequent than is reasonable, and are a severe threat. They lag the game, every shot they do after their first is 100% accurate, and if you have a passenger, you'll have to do a very long and drawn out fight scene, where death and/or failure (requiring a restart of the already Scrappy Escort Mission) is a very high possibility. Good news is, you can destroy the cannonballs they fire at you before they even make contact. Besides that, you can always slow the train down while carrying a passenger so that you lessen the risk of multitasking to both fend off the pirates and follow the signs.
The Spirit Flute duets have a small hatedom due to the item's incredibly finicky and picky nature.
Passenger missions as well, at least when you're forced to go through enemy-infested sections of railroad tracks. Your passenger will get increasingly annoyed with you each time the train gets hit, and fighting to keep the ship from being blown up by pirates apparently isn't a valid excuse for not blowing your whistle when a sign tells you to...
The Adventure Pouch. To elaborate, it's essentially a separate inventory where you can store up to 8 (with upgrades, up to 4 initially) items of your choosing. Except that said items are things that didn't even use up an inventory slot in previous games, like Shields and Bottles. By far the most irritating, however, is the way ammo expansions work. Rather than simply getting a bigger quiver/seed satchel/bomb bag that replaces your old one, you have to buy an extra quiver/bag/satchel and have it use up an inventory slot just to be able to carry even 10 extra bombs/arrows/seeds. Said inventory slot could be used for a bottle or even a shield. Oh, and in order to have a full life meter, you need to equip two 'life medals', meaning if you want it to look like you have 100% Completion, you'll need to use up two precious slots on those, effectively giving you only 6 slots to work with.
There's also treasure. When you pick up a new type of treasure, you get the usual animation of Link holding it up and a text box announcing what it is, followed by your tally of that item going up by one. All well and good, except that this aspect resets every time you start up the game; anything you haven't picked up in the current game session triggers the time-consuming cutscene all over again because, evidently, you are woefully incapable of remembering what a bird feather is between game sessions (or woefully incapable of looking it up on the inventory menu).
This game also inexplicably did away with adjustable text speed, uses a ridiculously slow speed as the default, and has more text-exposition than any other Zelda game, so be prepared to sit through many lines of tedious text, often text you've been force-read dozens of times already, every time you buy anything or talk to anyone for any other reason. Plot-relevant text is even slower. Holding down the A button speeds it up a tiny bit, but not nearly enough to prevent boring an average-speed reader to death.
The dash mechanic. Link's stamina can only be enhanced through temporary (andexpensive) potion effects, and given that Link walks so slowly otherwise, you'll find yourself constantly having to press the dash button just to get around. In addition, climbing walls and stuff now takes up stamina whereas in previous games you could take as long as you wanted to climb a wall so long as you didn't fall off. There are usually Stamina Fruits in both cases to mitigate the issue, but it still can easily trip up new players.