Speaking of Riolu and Naruto, the former is can apparently water-walk through the use of Aura by using "modified physics" to keep the surface tension from breaking. Ash flat out called it ignoring the laws of physics.
Brock's Ninetales and Growlie reenact the famous Spaghetti Kiss date scene from Lady and the Tramp. Lampshaded when the waiter asks his boss why they're serving spaghetti when it's a sushi restaurant and where the manager and cook learned to play the violin and accordion.
During his Gym battle with Sabrina, Ash calls himself the "inner babysitter." Lampshaded when Sabrina asks if he stole that line from somewhere.
James' guidebook is published by Prima. For those who don't get it, Prima is a company that makes video game strategy guides, including ones for Pokemon.
And then it gets combined with Adaptation Name Change and Mythology Gag later on. It turns out that Lorelei (whose name became Prima in the English anime dub) wrote those guides and gives lecture tours under that alias, so as to keep her Elite Four career separate from her scientific one, and actually wrote guidebooks for Pokemon trainers in the anime (shown when Team Rocket suggested her to do it and she announced the price).
When Dexter manifests a Porygon form for the first time, it says, "Stand by, ready. Set up." It later gains a projector based on Bardiche, and refers to one of its shapeshifting forms as "Sonic Form". Gary later gains a Porygon from his PokÚdex as well, and its projector is a red/purple sphere, aka Raising Heart.