Klingons, Harry Mudd, and the Alternate Universe.
Klingons:
Why Klingons have different looks over the last 50 years of Star Trek.
The straight up answer straight off the Memory Alpha wiki is that they couldn't budget costume effects for aliens in a easy way back then in TOS until season 3 which was the first time they could afford to actually make a Romulan makeup actor appear on screen.
So the bottom line of Klingons was, the makeup fit the budget. Till the films which had a larger budget to work with.
To make sense of this, The timeline will be set to Earth years and not release dates of shows.
°Enterprise:
~S04E04, Borderland: Dr Soong's genetically enhanced humans (known as Augments) held in prison since the Eugenics war escape and take over a Klingon Bird of Prey. The existence of Dr. Soong still living in a Federation 'Black Site' causes Captain Archer to assume responsibility for Dr. Soong to use the doctor to find and stop the Augments plans to finding and raising over 1000 genetically engineered brothers and sisters embryos.
~S04E05, Cold Station 12: Cold Station 12 is starfleet's basic CDC in the future where all super biological threats are stored and it's where the embryos of Dr Soong's genetically engineered humans are being kept. So that's where the escaped augments head to reclaim the embryos.
~S04E06, The Augments: All of the freed augments call Dr. Soong "Father" and he considers them his children and really does just want them to be better or at least okay. He was trying to make the human race better with no nefarious actions just less moral decisions medically. However being genetically altered the mindset of the augments is not the same as normal humans. So the leader of the augments and Doctor Soong or Father have differing issues of how to proceed.
~S04E15, Affliction: After the Klingons have their asses handed to them and their bird of prey stolen by the augments back on Borderlands episode. They begin to develop genetic manipulation to augment their soldiers as well the result is not what they expected at all causing side effects that even include physical outward appearance changes. It has become a pandemic spreading virus to the Klingons on the planet the development facility is located on. Dr. Phlox is kidnapped while on Earth and taken to the Klingon research facility where he is, as Klingons would put it, 'politely' threatened to fix the genetic failure in the serum and find a way to reverse it.
~S04E16, Divergent: The struggle to find a cure for the Klingon failure adjusting genetic manipulation continues Dr. Phlox and the lead Klingon Surgeon General working together have found a cure for future outbreaks that will stop from devastating the planet the virus had been released on and stopping its spread throughout the Galaxy. However this does not please General K'vavg. The military-minded Klingon Warrior and leader who demands positive results and not a cure but further augmentation of his soldiers. Dr. Phlox has managed to follow the Hippocratic Oath to the best he could to repair the DNA sequence. But cannot reverse the effects. But in one small breath of statement says "Ahead over many years things may return to the way they were." and almost as a joke the Klingon doctor that had worked with him the whole time considers out loud to not be the Surgeon General anymore but to go in cranial reconstructive surgery. As the augments were human, part of the serum had human DNA in it.
At this point in Star Trek Enterprise episodes the focus of genetic manipulation end. Now Enterprise's second tie-in with Discovery.
~S04E18: In a.. Mirror, Darkly, part 1. The crew of the Enterprise NX-01 are sent into a mirror universe, (as so many Star Trek shows before haha), The Narrative is similar, The Terran Empire rules all, and carries harsh sentences against people not willing to cooperate. Is also the first time that we get a glimpse of a constitution-class vessel that has been captured by the Tholians of this universe when it two was accidentally transported from the United Federation of planets universe we're used to. It happens to be the USS Defiant, a sister ship of the Enterprise NCC-1701. Without more spoilers. The main reason to watch this episode and it's part 2, S04E19 is that we see what a Tholian looks like for the first time as one has never been shown on any Star Trek show before only their ships and their screeching verbal communication. Oh, and luckily unlike Spock from Mirror Mirror in TOS alternate universe episode who has a goatee. T'pol does not have a goatee or much of a uniform.
(Season 4 Eps 20, ENT's final eps, Commander Will Riker walks out of a Halo Suite with Deanna Troi after finishing a program on the history of Starfleet)
°Star Trek TOS
~S01E07, Mudd's Women: Our first meeting with Harold Fenton Mudd (I believe) is this episode, where Kirk and crew rescue Harry and three young ladies from danger but it turns out that Harry's three female companions are actually mail order brides. Kirk as well learns of Mudd's reputation and tries to bring him to Justice.
~S01E23, Space Seed: Enterprise encounters the super human Khan Noonian Singh and his fellow augmented survivors of the Eugenics War from the Botany Bay. Powerful and devious Khan makes plans to eliminate Kirk and continued his mission of supreme dominance in the galaxy.
~S01E27, Errand of Mercy: War has officially been declared against the Federation and the Klingon Empire in an effort to save erase people from being subjugated by the Klingons Kirk and the Enterprise go to get negotiate with them. At the same time the Klingons show up and we meet a Klingon for the first time as Kirk and the Klingon stand side-by-side in front of the Elder Council of this planet.
~S01E28, The Alternative Factor: Kirk meets Lazarus, who claims he is chasing his parallel self through space and time and if Kirk doesn't help him the entire Multiverse is at risk.
~S02E04, Mirror, Mirror: Kirk, McCoy, Scotty and Uhura find themselves in the Mirror Universe aboard the parallel ISS Enterprise run by ruthless ideals of the Terran Empire.
~S02E08, I, Mudd: apparently after Harry muds unsuccessful attempts of taking the USS Discovery from Captain Lorca he has now decided to return and take over the Enterprise by stranding the crew on a planet populated by Androids under his control.
~S02E11, Friday's Child: the Federation is once again in competition with the Klingons for an alliance with the inhabitants of Capella 5 home of a Warrior tribe.
~S02E15, The Trouble with Tribbles: Kirk and the Enterprise are tasked with protecting shipments of grain at a neutral Space Station when a Klingon battle cruiser also docks for Shore leave tensions grohi. And to top it off a peddler Harry Mudd infest the space station with Tribbles a quick reading furry pet like creature that also hate Klingons even though they're the size of a rodent.
~S03E07, Day of the Dove: (In this episode we get our first glimpse of Klingon men and women interacting.) As an entity traps the Enterprise crew and the Klingon crew in an unending War aboard the Enterprise.
~S03E09, The Tholian Web:
(Discovery double tie-in)
A first glimpse of Tholian ships and tactics using their web designed weapon. Kirk and the derelict Starship Defiant vanish into a spatial interface between universes. Tying back to ENT and the 2nd half of Discovery, where the Tholians have the constellation-class USS Defiant.
°Star Trek TNG
Now in the 24th century, a few centuries after the Klingons attempt to create their own augmented Warriors failed. And Captain Kirk defeating the remaining augments following Khan in the movie Star Trek II The Wrath of Khan. Klingons have now joined the Federation as allies. Even Worf, the first Klingon to join Star Fleet, is a bridge officer on the flagship of the Federation, the USS Enterprise NCC-1701 D.
The genetic changes to the DNA in the Klingons have receded, as their larger stature, cranial ridges, and receding hairline, have returned. (This is my way of making the Klingon changes part of the story and not only just the low budget of a television company)
The topic of the Klingon look isn't brought in TNG.
Harry Mudd would have passed away by now. But, the alternate universe is still in play. But, I will still search TNG and add the episodes in time. Similar events like the Q continuum, and the being called The Traveler teaching Wesley Crusher how to phase leave me to believe that I'm sure over the 7 years there is an episode or two where TNG visits the Mirror Universe.
°Star Trek DS9
~S02E23, Crossover: After experiencing operational difficulties while traveling Through the Wormhole Kira and Bashir find themselves in the alternate universe.
~S03E19, Though the Looking Glass: Cisco is abducted by a double of O'Brien, who takes him to the Mirror Universe that Kira and Bashir visited a year earlier.
~S05E06, Trials and Tribble-ations: After Darvin, a disgraced Klingon spy, travels back in time to alter some events to his liking. The crew of DS9 including Worf find themselves back in time during the same events on the station with Captain Kirk's Enterprise crew and the Klingon crew from S02E15, 'The Trouble with Tribbles'. Seeing the difference in appearance of the Klingons from the past, O'Brien looks at Worf, and Worf just turns and quotes "We don't talk about it."
This is the last time so far that anything involving the different appearances of Klingons is mentioned.
°Star Trek Voyager
Not present in any particular season or episode of Voyager, the only physical appearance changes in any Klingons are Borg assimilated Klingons. Just as all other assimilated races by the Borg have a change of appearance.
However, on Star Trek Discovery, the Klingons also experiment with species re sequencing to put spies in the Federation by mutilating Klingons to look human but this seems to have only occurred with one individual.