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.
Badass Decay: Well, design wise, compare the fierce Rodan design in the original film to the goofier one in Monster Zero.
King Ghidorah in Godzilla vs Gigan is often seen as this.
Zilla. One of the main reasons he is viewed so negatively by the fans.
Averted in Zilla Junior's case, when fans consider him the best incaration.
Weirdly averted by Godzilla himself: the more he ceased being a true monster, the more he moved into Crazy Awesome.
Base Breaker: Godzilla Final Wars. It's not uncommon to find completely polarizing opinions on this film from many fans to the point that it's mentioned as one of the best entries in the series as much as it is mentioned as one of the worst.
Big Lipped Alligator Moment: Some consider the entire film of Godzilla vs Hedorah to be this, peaks with the flying scene. Also the talking scene in Godzilla vs. Gigan.
Godzilla's Revenge, which takes place entirely in a boy's imagination, and has Minilla facing a bully and interacting with the boy (complete with goofy "hyuk-hyuk" voice).
How about the weird hippie couple in GMK, seen just before Godzilla enters Yokohama?
Maguma's entire appearance in Gorath. So much so he was cut from the American dub entirely.
Complete Monster: Gigan and Ghidorah, a pair of forty-story psychos for hire with a penchant for destroying entire civilisations, and torturing their opponents.
Crowning Moment of Awesome: Godzilla has a lot of these! His dynamic entrance in Terror of Mechagodzilla, to shooting a blast down Biollante's throat!
In Mothra vs. Godzilla, and again in Godzilla: Tokyo S.O.S., despite being old, on the edge of death, and being very frail, Mothra agrees to battle freakin' Godzilla and gave everything she could to try to stop him, resulting in her tearjerking death. Also see Visual Effects of Awesome.
Ensemble Darkhorse: With a robust roster of monsters, there are many of these, and nearly every monster is a fan favorite in certain sectors. However, probably the best two examples would be Anguirus, particularly for American fans, and Baragon, particularly for Japanese fans.
Despite only appearing in the first movie (and, even there, having limited screentime) Dr. Daisuke Serizawa is easily the most famous human character in the series.
Megalon. Despite appearing in one movie, he is one of the easiest monsters to play in the Godzilla games. Easy to use in combat and great for beginners no matter which system you're playing.
Despite being scrapped, the Rat/Fish monster Deutalios is popular due to the Toho Kingdom toons.
Mechagodzilla proving to finally give a serious threat to the series after a long period of goofiness made it one of these, enough so to return for another film and return in every subsequent movie series.
Biolante and Destoroyah both proved very popular despite only appearing in one movie.
Fandom Heresy: Criticizing the original film. No matter what your opinion of all the other films are, you're asking for an ass-kicking if you insult the original on any forum.
wait! if you listen carefully at it, it reminds A LOT of a psychotic giggle. kinda fitting for a planet-destroying monster.
MST3K Mantra: It's just best not to think too hard about a film series that stars giant radioactive dinosaurs, three-headed cyborg dragons, giant butterflies, giant cyborg monsters from outer space, etc.
Rescued from the Scrappy Heap: There's the animated Godzilla series that rescued Gino, the one that actually had Godzilla's powers; then done again in Final Wars that accepted Gino as Zilla into the franchise, even if it was a Curb-Stomp Battle. Baby Godzilla and Godzilla Junior showed that Godzilla having a son wasn't a bad idea if executed right. In recent years with the original version of Gojira becoming better known in the States there has been a backlash against King of The Monsters. However numerous historians have pointed out that Godzilla would not be so well known if not for King of The Monsters. Even Raymond Burr as been redeemed somewhat in fan's eyes when it was revealed he refused the comical lines and played his reprisal in Godzilla1985 with dignity.
Sacred Cow: As noted above, it's widely agreed that the original film is a masterpiece and criticizing it is rare at best. Even people who hate Godzilla movies tend to agree that it's good.
So Bad, It's Good: While this designation applies to much of the franchise, the films in the seventies are particular prone to falling under this sort of designation with plots, monsters, and dialogue that is outlandish even by the regular standards of the series.
Special Effects Failure: Fairly common among many of the movies, although surely the worst are Godzilla's Revenge, Godzilla vs Gigan, and Godzilla vs Megalon, which all include a hefty amount of stock footage.
Surprisingly Improved Sequel: YMMV a great deal of course, but the most commonly cited would be Destroy All Monsters over Godzilla vs the Sea Monster and Son of Godzilla, Terror of Mechagodzilla over all of the other 70's films, with a tiny window of Hedorah over Revenge, and 2001's GMK over Godzilla 2000 and Godzilla vs Megaguirus. Many fans would also say this for War of the Gargantuas, which is a cult favorite over it's much more forgotten predecessor, Frankenstein Conquers the World.
Vindicated by History: Terror Of Mechagodzilla had the weakest performance of the Showa era, but today is a fan favorite and is often seen by many fans as the best of the 70's Godzilla films.
Visual Effects of Awesome: There are many instances, and YMMV a lot as usual, although the battle between Godzilla and the adult Mothra in the 1964 Mothra vs Godzilla is a timeless fan-favorite, and usually seen as one of Tsuburaya's crowning achievements.