Goofs

Goldar has wings in Day of the Dumpster (the official first episode.) These wings disappear in all subsequent episodes (of the first season) for no apparent reason.

In some episodes, the school principal's name is spelled Caplan, while in some others it is spelled Kaplan.

Zack is missing his middle finger on his left hand, but he has it when in ranger form.

In Day Of The Dumpster (the first official episode of the series), the Rangers are shown with their wrist communicators on. They didn't gain these until a later episode.

When Rita's spell on Tommy/Green Ranger is broken, it is revealed that they can form a new Zord by combining the Dragonzord, Mastodon Zord, Saber Tooth Tiger Zord, and the Triceratops Zord. When introduced this is called "Dragonzord in Fighting Mode" or "Dragonzord in Battle Mode." In subsequent appearances, this is called the "Mega Dragonzord." Further adding to the confusion, the "fighting/battle mode" name returns later on, and Mega Dragonzord comes to mean an entirely new Zord, which is essentially the Dragonzord laid over the Megazord. It is also interesting to note that Jason and Kimberly appear in the fighting/battle mode cockpit, even though it does NOT use their Zords.

Episode 93 "Lights, Camera, Action" claims that David Sarnoff invented the television. While the actual inventor is a matter of debate, David Sarnoff in fact simply ran competing company RCA; he never did any actual inventing.

The battle footage is composed of Japanese footage from the Zyuranger Super Sentai series. This normally is not a problem, but if one looks closely, there are a few scenes where the word "Zyuranger" can be seen on the Rangers' Power Morphers/Blade Blasters/Weapons/etc.

In episode 72, "Green No More Part I", Lord Zedd has captured the rangers in an energy field, while he walks around gloating. Duct tape is visible on his staff just below the "Z" presumably broken during rehearsal because it is used to fight a powerless Tommy later.

At multiple points in the "Return of the Green Ranger" 3-parter, gum trees are visible in most of the 1770s scenes. These trees are native to Australia, but the show is set in California.

Secret identities are traditionally used to protect a hero and their loved one's from their enemies, yet the identity of the Power Rangers is ONLY a secret to their loved ones - literally every enemy they face (in this and following series') knows who they are. In fact, they quite regularly form plans based on an individual Rangers' phobias or personal items.

Rita can apparently see anything anywhere on Earth, and knows the Power Rangers' secret identities. Since she has this information, why was she never able to beat the team? She could easily have sent down multiple monsters to kill the Rangers while they were sleeping.