Ear Worm: There is a certain catchy flavor to the theme song, about how "Victory is ours forevermore!" Many fans consider it one of the best themes Power Rangers has ever made.
Also, around this time, Emma Lahana (Kira) was attempting to launch a music career; her self-penned music was used on different occasions, as well as being available on her website. The songs "Freak You Out" & "Patiently" in particular, were rather catchy.
To further emphasize this: she is the not just the only female, but the only ranger period to fight with 2 veteran rangers, the only Yellow Ranger to appear beyond her core season without her teammates, and has shared screentime with more rangers than any other female in the entire franchise. Not bad for a Disney era ranger! Especially when you consider she operates under the same team with Tommy... Come for Tommy, stay for Kira is pretty much a proper description here.
Hell, to an extent, all the rangers are some of the most loved in the franchise, especially as a team. There's a reason many fans consider this the Time Force of the Disney Era, and many were subsequently annoyed when no Dino Thunder actors were brought back for Super Megaforce (Tommy only wore his Green Ranger outfit).
Mesogog is one of the most beloved villains since Ransik. His complete monotone behavior for the majority of the season combined with his sheer creepiness factor helps out.
Fan Wank: How Tommy got that PhD in archaeology in the first place. A theory goes that when he had his brain scrambled by Prince Gasket in Power Rangers Zeo, he gained the ability to detect temporal anomalies and (briefly) see into the future. Thus, the ability to see the future also allows him to see the past, giving him near-perfect historical knowledge as well as just generally boosting his intelligence.
Hilarious in Hindsight: Tommy's morpher this season is a two-piece device that requires him to insert a key into a wrist brace. This is the same setup as in Gosei Sentai Dairanger, which only got one of the six Ranger suits in Power Rangers. Guess who wore that suit?
It's also the same setup for the Turbo Morphers.
In "Fighting Spirit", three Rangers, one red, another white, the other green, gave their powers to someone in a near-death experience. The same thing happens to Gai in Kaizoku Sentai Gokaiger. Bonus points for the Green Ranger being the same one in Gokaiger.
And the White Ranger in the Gokaiger scene is the one from the Sentai for this series.
It Was His Sled: Tommy being the Black Ranger. No one on this site even attempts to hide it, but it's justified, as everyone called it when it was announced he was coming back.
Jerkass Woobie: Zeltrax in "Golden Boy" inadvertently created his son, Goldenrod. Zeltrax decided to use him to help destroy Tommy, and would grow to accept him as family. Unfortunately, he watches his son be destroyed by Tommy. He mourns the only family he had while getting another reason to hate the Black Ranger.
Most Annoying Sound: This season used a lot of stock music, and hearing it over and over again could get grating after a while. Even the theme song could be this, given how nearly all the Megazord fights used it as background music.
So Bad, It's Good: The dub that takes up most of "Lost and Found in Translation". Absolutely hilarious.
Special Effect Failure: The shields on the Green and White Mighty Morphin' suits that were used in Fighting Spirit seemed to be coming apart during the fight scenes. This is likely because the suits were bought from a museum to use for the episode and were likely created for displaying rather than actual stunt work. (this may also count for why the suits weren't 100% show accurate either e.g the silver trimming of the green helmet).
Or it could be that he's taken a few blows to the head over the years and the memory has gotten a little fuzzy.
Mesogog's bobble-headed final form (the "Mesomonster" in the credits).
The Valkasaurus Megazord has the Triceratops mouth at the end of one arm, and the T-Rex tail at the end of the other arm, except for when it attacks the monster - then it has hands that hold its battle axes. You can blame Abaranger for that, though.
Strong as They Need to Be: Trent is the strongest Ranger after he joins the good guys (as is typical for Sixth Rangers), except for the episode "Fighting Spirit" in which suddenly Tommy is stronger, just because the episode is about how awesome he is.
Take That, Scrappy!: "Day of the Dino: Part 2" and the "Thunder Storm" two-parter show Mesogog blatantly calling Lothor a joke.
They Wasted a Perfectly Good Plot: Trent as the evil White Ranger is capable of giving a serious beatdown on the other Rangers, viciously freezes Tommy in amber, and is basically a terrible threat. So then they lay off, have him temporarily turn good because of the meteor's influence, fighting Zeltrax for position... basically doing everything but living up to the badass threat he first posed to the good guys. It's especially disappointing when they really had no need to turn him good so early, other than to retread Green With Evil, so that they could continue to accommodate his Sentai counterpart's continued villain status until the end.