Little Nemo provides examples of the following tropes:
Abusive Parents: Nemo's parents threaten to spank him for things that he does in his sleep that he really has no control over, like falling out of bed, yelling in his sleep, and even kicking the covers off his bed. Pretty standard parenting for 1905.
Comic Book Time: Although it's also heavily Lampshaded at times, with characters complaining they feel like they've waited "for weeks" for something to happen.
Cyclic Trope: McKay enjoyed a publishing environment that allowed an extravagant art style that subsequent generations of sequential artists would be unable to approach until Web Comics became practical.
Floorboard Failure: In Little Nemo in Slumberland, Nemo and Flip are served a new kind of breakfast food that gives them a Balloon Belly. The chairs start to collapse underneath their weight, and then the floors, leading to the entire house being demolished.
For the Evulz: Pretty much Flip's entire motivating force, at first.
In one comic there's a giant named Boob. Hearing someone say "Wait until I see that Boob!" can make modern readers chuckle.
"I want to stop and rest a bit, I'm fagged out from running!"
Heel-Face Turn: Flip does one in the comic, starting out as the main antagonist by waking Nemo up from his dream to eventually becoming Nemo's friend. Though he was never really "evil" per se, but more of a nuisance. Much later in the comic, he went back to being a nuisance again. Being a nuisance was only the beginning for Flip. His vindictiveness was what caused the real damage. Whenever the people of Slumberland took measures to keep him from ruining their events by being a major nuisance, he retaliated, often ending up wreaking havoc on parts of Slumberland (or having his uncle melt them). At one point, he has his uncle melt down the whole city. Oddly enough, this same tendency is what also what starts his Heel-Face Turn as he saves the group after they're captured by pirates.
In one installment, Nemo, Flip and Imp are so hungry that they begin tearing off lines from their comic panels and knocking down letters from the Little Nemo in Slumberland logo, eating them. Nemo worries that this will upset the artist but Flip maintains that it will teach the person who draws them a lesson. When Flip asks what's in the letters they're eating Nemo replies that it's printer's ink as far as he knows.
And something similar happens in this comic, where eventually the entire panel collapses on itself and Nemo complains to the artist.
Recurring Dreams: The entire comic. Suffice to say, if your dreams keep continuing every night as an ongoing story arc, it's time to see a shrink.
Remember the New Guy: The Professor mainly debuted this way because he was first introduced in a popular Little Nemo stage show based on the comics, which also makes him a Canon Immigrant.
Save the Villain: When Flip was still the antagonist Nemo did save him a few times, most notably when King Morpheus' firing squad was about ready to execute Flip, and Nemo ran in front of him to stop it. Of course Flip was less than grateful, because in the next installment he convinces his Uncle Dawn to bring forth the sun and ruin the King's Thanksgiving dinner by waking everyone up.
Show, Don't Tell: Boy howdy, in the early strips this is averted right into Viewers Are Morons territory. The running captions explain every little detail that you can either plainly see or can infer with only minimal brain-power.
Sky Pirates: They attack the royal airship in one installment.
Spiritual Successor: Before Nemo', McCay wrote a strip called Dream of the Rarebit Fiend'', which was about random people having surreal dreams thanks to eating Welsh rarebit (a kind of cheese stew).
Taken for Granite: Nemo is turned into a statue for a week to hide him from Flip in one issue. And the next week Flip gets turned into a statue.
There Are No Therapists: You'd think that Nemo's parents would try to get some sort of help for him, seeing as he appears to wake up screaming from nightmares every night, or at least stop feeding him the food they keep blaming it on.
Vague Age: We never find out just how old Flip is. He's sometimes referred to as a child, and he's certainly the same height as Nemo, though he has a receding hairline and smokes cigars. At one point he claims to be 23 years old but even that is debatable.
Walk the Plank: In an issue where Nemo, Flip and the princess are abducted by pirates.