The Mario, Kirby, and other Nintendo guest stars in Link's Awakening seem a lot less out of place when you realize it's all just a dream. Even better if you pay close attention to the cameo enemies. Most were from Super Mario Bros. 2, which took place in a dream world called Subcon, and Kirby is, well, from Dream Land. It's lighthearted foreshadowing.
Tarin (an expy of Mario) turning into a Tanuki makes a lot of sense if you consider the Tanuki suit has been a long-standing power-up in Mario games.
Likeways the cameo of Luigi as the chicken breeder that can help you find the Flying Rooster (and adopts it after Eagle Rock) makes sense if you consider Luigi's signature ability in the franchise: his floaty jump.
Why did the Item Get! jingle play when Marin joined your party? Because you two became an item! He even picks her up and sweeps her off her feet (literally!)
Why do the Shadow Nightmares take the forms of Agahnim and Ganon? Because this game's Link is the same one who fought them in A Link to the Past, and they've haunted his nightmares ever since.
Alternatively, it is a different Link, and they've haunted him across lifetimes.
Why is the boomerang so powerful compared to the rest of its counterparts? It's a dream. It's possible Link secretly wished the boomerang was more powerful, and the dream picked up on it.
The Nightmares take on the form of Agahnim and Ganon in the final battle because they're exploiting Link's personal fears and experiences in a vain attempt to defeat him. When that doesn't work, they turn into Death Eye and wildly swing in a last-ditch effort to try and defeat you.
Also, in Link's Awakening the only way to damage the Nightmare Ganon is with the Spin Attack or Pegasus Boots. Regular sword attacks and no other weapons will work. Why? Not only does Link no longer have the Master Sword, (having returned it to its pedestal) but unless you've fully upgraded it to the Golden Sword you can't damage Ganon with a regular sword attack in A Link To The Past, either, and have to rely on the Spin Attack to damage him.
The other Nightmare forms also make sense - The Slime is a monster that Link can't damage with his sword. Moldorm was considered That One Boss. And of course Lanmola was a last-ditch effort before becoming DethI/Death Eye.
Wind Fish is a Nintendo fan. If he dreamed about all those Nintendo-characters and cameos so much, it has to reflect to his true nature as well.
Why does the game go out of its way to mention at the beginning that Link's name is on his Shield and Sword, and that the game suggests he write his name on the Koholint Sword when you get it? Because of his encounter with the Tokay back in Labrynna, where he shipwrecked onto their island and they took away his items that were laying on the ground, not knowing/realizing that they were actually his.
Why do whatever monsters kidnapped and abandoned Marin not even try to get her back after Link rescues her? For that matter, why was she kidnapped in the first place? She's part of the Wind Fish's dream. The Nightmares probably kidnapped her specifically so Link would save her, sparking a romance that they hoped would lead Link to abandon his quest.
Alternatively, they know she ISN'T part of the dream if one WMG is true; she's the only one to question what's outside the island, and finding out means waking the Wind Fish. Being a seagull (or something) that will survive, they don't want her giving anyone ideas.
Why does the Shopkeeper shoot lightning at a thieving Link? Think about how Link got to Koholint Island in the first place. As far as the Wind Fish knows, the last thing Link saw out there is probably the last thing he sees here.
When the game begins, it mostly features rather familiar Zelda elements. As you progress onward and unlock more of the island, you encounter more and more bizarre things. Like the owl said, the Wind Fish grows restless - As Link collects Instruments, the dream world slowly loses its illusion of reality and begins falling apart. It's even possible that the face shrine never existed until Link actually saw it with his own eyes, and is a result of a metaphorical mask crumbling away.
The Frog's Song of Soul sounds noticeably funkier in the remake. They're frogs. It's hip-hop.
DeathI's final form using the mini-boss theme in the Game Boy versions actually makes sense: The previous Nightmare forms during the Boss Rush are incarnations of Link's past foes, enemies from his own nightmares. With DeathI making a last-ditch attempt, it reveals its true form: something Link had never previously seen, much like the mini-bosses and most of the Nightmares on Koholint.
With the addition of shapes to the Color Dungeon, the defense-granting blue tunic gains an extra layer; within the dungeons, the shape most frequently associated with blue is a square. Thus, the blue tunic is a block tunic in more ways than one.
Every piece of text and dialogue in the game is italicized, which stands out from every other Zelda title, particularly the Oracle games, which are made using the same engine but use regular-styled text instead. Of course, italicized text is usually used to indicate that it's something a certain character is thinking, and what is Koholint Island but a completely mental construct thought up by the Wind Fish's mind?
In the remake, the reason why the Face Shrine's music is so melancholy is obvious given what happened immediately before. But there's a very sneaky aspect to it: when the original theme finally kicks in, it's ripped directly from the original version of the game, juxtaposing an emotional song with a video-gamey one. What better metaphor for the revelation that none of this is real?
Also in the remake, the art style has been a point of contention, however you'll notice that during the opening and ending cutscenes, Link as well as the vision of Marin in the secret ending appears in a more "realistic" style instead of the toy-like one seen during the rest of the game. Why is this? Well, toys are often used to play out fantasy scenarios.. very similar to what one can define a dream as.
Look closely on the screen where you fight Angler Fish, and you can see a skull in the background among the rocks. After you complete the dungeon is when the ghost starts following you.
The game ends with Link out at sea on what remains of his boat. That's the last time we see that Link. Whether he made it back or not is left to a player's interpretation.
Don't forget that in the secret ending, which is presumably the canonical one, he has either a winged girl or a presumably-still-sapient seagull who knows he's out there. Marin will probably guide him safely to dry land, or she could carry a message to someone so that they know to go and rescue him.
You discover the truth about Koholint Island just before the Face Shrine. The boss, Facade, even tells you point blank that the island isn't real. You're seeing Koholint Island's true face.
