The ending to "Deal with a Nighlok", when Jayden manifests an image of Ryan's father, who's stationed overseas, to encourage him to do his best in his baseball game.
"Jayden's Challenge", Jayden comforting a little boy who's father is away at work, causing him to remember what happened to his father.
From "Unexpected Arrival", Jayden reuniting with his childhood friend Antonio after so many years. Always nice when friendships are unhindered by distance or lack of contact.
In "Team Spirit", the entire team is willing to become Nighloks so they can enter the Netherworld to get back Emily's spirit/soul.
In "Broken Dreams", Mia sees glimspes of Dayu's past. Here, we see Dayu and Deker going into their new home a happy couple and we see them exchange gifts... a samurai sword and a guitar. Then everything goes down in flames.
Bulk and Spike's giddy greeting in "Origins, Part 2."
"My favorite nephew!"
In "Runaway Spike", Mia spots Spike sitting nearby after a battle and talks to him, letting him vent on how he's been fired from three jobs that day and how could he ever become a samurai if he can't even hold down a job. She then proceeds to cheer him up by telling him to keep trying and that a true samurai never gives up.
The reason Spike had those jobs in the first place? To try and help his Uncle Bulk pay their overdue rent.
Bulk and Spike get a very special present in "Stuck on Christmas": a personal visit and thanks from all five core Samurai Rangers.
Lauren giving Mike the Shark Disk in The Sealing Symbol. Throughout the show, Mike was constantly shown as the least skilled member of the team. What better way to cap off his Character Development than by letting him use the most powerful Super Mode (outside of the modes used for piloting the Zords) to fight Xandred?
Mike and Emily together. It's interesting because Emily took up the samurai sword due to her sister becoming sick, following her sense of duty. Mike was part of a samurai family, yes, but he was also the least traditional of the team, enjoying games and goofing off. Yet somehow the two of them ended up forming a bond over their desire to be as good as people expected them to be, and in the finale walk off as an Official Couple. (kinda)
A meta one: during a Q&A, the Samurai cast were asked which past ranger they would most like to team up with. Hector David JR, who plays Mike, said he would most like to team up with JDF and do a Forever Green episode. come Super Megaforce, one of the behind the scenes photos shows JDF and Hector in their Green Ranger suits... and JDF has lent Hector his Dragon shield which Hector is wearing over his Samurai suit! It's almost definitely not going to actually show up in the show itself, but it's really nice to see this moment between the original and most recent Green Rangers.
Jayden's appearance in Super Megaforce shows him riding his own motorcycle alongside Mentor Ji, showing that he has been successful in getting the Ranger to learn to have fun.