These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Bulk & Skull, the only original cast members left, had their popularity confirmed with their Crowning Moment of Awesome at the end of the season.
The Psycho Rangers, for giving Evil Counterparts to the Power Rangers that were finally characters with individual personalities and villains in their own right rather than just a cheap Evil Knock Off. They're sheer badassery also helped. They were popular enough to have a trope named after them. Even 15 years later, the fact that they were never made into action figures is still a sore subject in some parts of the Ranger fandom.
Evil Is Sexy: Melody Perkins as Astronema gained quite a few fans from this series.
Fanon: The United Alliance of Evil being the name of the collection of Big Bads. It actually comes from a throwaway line in Power Rangers Zeo about King Mondo having broken away from something called the United Alliance of Evil - just who and what that is isn't expounded upon, and the name is never used at any other time. It makes a pretty good name for PRiS' villain group, but Canon it's not.
Also in most stories where Karone becomes a ranger as opposed to canon she will usually be the purple ranger based on the color of her honorary ranger outfit.
"Funny Aneurysm" Moment: "When Push Comes to Shove" and its 9/11 analogues. The episode featured Cassie and a guy she's on a date with trapped at the top of the tallest building in Angel Grove as a beast is trying to knock it to the ground, trying to send Angel Grove up in smoke.
Good Troi Episode: "True Blue to the Rescue" is looked upon as a good Justin episode, not only resolving dangling plot lines from the end of Turbo but providing a more proper parting between the characters.
Growing the Beard: It was shocking how effectively dramatic this show got (while still having the cheesy charm of the overall series). This is especially noteworthy as it came after the unpopular Turbo.
For this particular series, the major storylines and dynamics of the season, such as the characterization that makes Ecliptor a fan-favourite, really all hit their stride once Darkonda shows up. There's a lot less filler from that point on.
Harsher in Hindsight: There is an entire episode that focus on Astronema using a monster to attack a building with people inside and cause it fall over. Of course this is Power Rangers so everyone survives, but imagine the writers trying to get this episode off the ground post 9/11
Hilarious in Hindsight: Astronema's "I wouldn't want to be a Power Ranger anyway!" Numerous production issues resulted in the actress becoming the Pink Ranger halfway through the next season.
Kind of a meta example, but in the full version of the theme song there are the lyrics "Long live the Power Rangers." To elaborate. "In Space" was meant to be (and was in fact written as) the finale of Power Rangers as a franchise. This addition to the lyrics reflected this mindset, but if one looks at it from today and notices the 12+ seasons that followed...
Moral Event Horizon: Dark Spector threatens to wipe out all life on Earth with a giant asteroid if the rangers don't turn Karone back over, and even after she's brainwashed, he lets the asteroid continue on its course anyways.
Justin's return episode helped ebb a lot of the anger at his character, as despite everything he represented (an attempt to appeal to the kids), he was still a Ranger, a member of the team and there was some genuine emotion between all of them.
Most returning Rangers from Turbo are seen as that.
They Wasted a Perfectly Good Plot: Despite numerous bits of foreshadowing, Dark Specter never finds out about Astronema's plan to drain his energy with the Psycho Rangers.
Tough Act to Follow: Every season after in Space has essentially been trying to copy the magic that made this season work. Some have managed better than others, but one major advantage this season has had over the others is the returning characters and strong mythology and continuity nods. The standalone team, standalone season format makes it more difficult to escalate the action and develop the characters.