The Hero: Although he rarely, if ever takes on the dominant role of leader, and even then under protest.
Law of Chromatic Superiority: Averted - despite getting a Cool Bike only for himself, he's the first Red Ranger in since In Space (For those not keeping track, that was ten seasons prior) to not get a Super Mode (Unless you count the armor he wears whilst riding said bike). He gains a second master last and earns his Master stripes later than Lily and Theo.
Rookie Red Ranger: Possibly a deconstruction, as he constantly worries about not being able to catch up to Theo and Lily. This, not lack of ability is what holds him back until he learns to let got of it.
The Big Guy: His fighting style is almost entirely hand-to-hand, and he's one of the most experienced fighters.
Composite Character: of Gekiranger's Gou (Geki Violet) and Sha-Fu, even though the latter's counterpart is Master Mao - but since Mao dies in the first episode many of Sha-Fu's early stuff gets shifted to R.J.
Spiritual Antithesis: To Tommy in Dino Thunder. Both juggle day jobs that involve being the rangers' superior, both become rangers after three and both are the most experienced fighters. However, while Tommy was a former ranger and was very direct and serious from years of being a Power Ranger and insisted in training on martial arts, RJ is more casual and laid back and prefers to use the mundane to show how they are effective training methods.
Take Up My Sword: A variant. In an episode where Lily is acting like a Jerkass thanks to the Monster of The Week, Fran snaps her out of it by threatening to take her morpher and help the Rangers. She only doesn't do it because the resulting brawl between her and Lily causes said snap-out.
Eldritch Abomination: Probably has the most qualities of one out of any Power Rangers villain besides Dark Specter. He's less an entity and more a demonic spirit for most of the series with immense power, even being able to rip open a portal to the afterlife to revive his minions once he regained enough of his true strength, and his true form is a gigantic eight headed dragon that's not even close to humanoid. In addition, we never find out exactly what he is or where he came from.
Parental Abandonment: During his childhood, his parents weren't around much, and he had to stay with a neighbor most of the time.
Sealed Evil in a Can: He has been stuck in an (unlocked!) box for 10,000 years. The box was kept by a secret order, but opened when a disgruntled student barged in and attacked the order's master, knocking the box out of his hands. Unusually, however, Dai Shi is significantly weaker than he was, and has to struggle to regain his powers before the Rangers become strong enough to destroy him.
You Have Failed Me: He strips Whiger of his Rinzin, title, and rank and banishes him from his temple as punishment for his defeat by the hands of the Jungle Master Stampede Formation.
You Have Outlived Your Usefulness: He allows the Rangers to destroy Carnisoar and Grizzaka and the Phantom Beast Generals to destroy Jellica because they are no longer needed by him now that he has learned to harness his hatred and deceit thanks to Carnisoar and Jellica and has learned Zocato on his own.
Undying Loyalty: Stays loyal to Dai Shi even after he abuses her, and even gets deposed.
Villains Out Shopping: Once she went to visit Jungle Karma Pizza when Dai Shi was giving her a hard time. She didn't find out the rangers's identities at the time, but they did help plant the seeds of her redemption.
Smug Super: His arrogance about his immense power and his claims to be completely invincible are good reasons why he counts as one.
The Starscream: Naturally, he blames Dai Shi for losing the war 10,000 years ago and hates humans even more. This makes perfect sense as, after being revived by Camille, he, upon arriving at Dai Shi's temple, is surprised to see that Dai Shi is now using the human Jarrod as a vessel. Jarrod wants Grizzaka to teach him Zocato, but, naturally, Grizzaka isn't too thrilled about that and simply refuses to take orders from any human. Guess what he does next?
Interestingly, out of all the Starscreams in the Power Rangers series, he is one of the few who actually succeed in overthrowing the Big Bad, and after his success, he becomes the ruler of the other evil forces until Dai Shi returns and takes back his throne.
This Cannot Be!: He screams this after the rangers destroy him with the Jungle Master Stampede Formation.
This Is Unforgivable!: Before his huge battle with the Rangers, he declares to them, "You destroyed all my warriors, my royal guards, and the great Overlord Carnisoar. Finally, I shall destroy you!"
Unstoppable Rage: Even Dai Shi and the other villains are wary of pissing him off.
We Meet Again: He says this verbatim to the Rangers before their huge fight in his last episode appearance before the finale.