In The Stinger to Yoshi's New Island, Mr. Pipe's revealed to be Adult Mario in disguise. While the adult Bowser and the modern-day Kamek time traveled to the past to Set Wrong What Once Went Right, Mario, in turn, was making sure the timeline went exactly as it happened by helping Yoshi and his baby counterpart with their tasks disguised so that they won't recognize him.
World 2-3 in the original, "What's Gusty Taste Like?", does some clever foreshadowing as to what to expect in 2-4 and 2-8. Gusty itself is a ghost. The boss of 2-4 is Bigger Boo, who is a giant ghost. The boss of 2-8 is Roger, who is the titular Potted Ghost owning the castle.
In Super Mario World, Mario rescues the Yoshis as he goes to rescue Peach. In this game, the Yoshis are aiding Mario to help him reunite with Luigi. They helped him in his time of need as a baby, so now as an adult, he's helping them in theirs.
At first, it may seem odd that the secret stage of World 3 starts you out in a jungle area only to throw you into an area not unlike something out of World 4 halfway through, until you realize that it could just mean Yoshi is leaving World 3 and entering World 4. Likewise, the secret stage of World 6 ends in a meadow-like area not unlike what you would see in World 1, which could mean Yoshi is ending his adventure and returning to World 1. The beginning of World 4's secret stage also looks very similar to the area where you fight Hookbill the Koopa. All of this implies that the secret stages are meant to be "epilogues" to their corresponding worlds.
The fight against Prince Froggy in the original. It seems like quite the humorous battle...that is, until the end, where you slide straight out of Froggy. Of course, there's the obvious. Froggy craps out Yellow Yoshi. Sure, it doesn't seem bad from our point of view, but imagine what Yellow went through. The look on his face as he's freed from Froggy's stomach says it all...
That's not even considering the fact that you destroyed the uvula and ruptured the organs of a frog, which leaves said frog writhing upside-down in absolute agony (if he didn't die).
If Kamek wants Mario alive, why did he let a frog swallow him? If it's dangerous in there for Yoshi, it must be just as dangerous for a baby human.
It's true that cognitive memories don't begin to form until past a certain age, but even with that in mind, how much trauma did Baby Mario exactly go through during the trek across Yoshi's Island? Of note is the fact that he was exposed to Fuzzies, which are practically hallucinogenics.
