Despite being one of the most important and influential relationships of the Dragon Ball franchise, the story of how Goku and ChiChi became "husband and wife" is unfortunately a low point in the anime's storytelling.
There are many reasons why anime adaptations of manga include filler arcs or storylines that are not included in the manga. For instance, filler arcs are often used when there are differences between the manga and anime scheduling where they both arrive at the same point in the story. Filler arcs are produced to "fill" the time it will take for the manga to create new content. Generally, since filler arcs are not canon, and tend to tell stories that take the story in unheard-of directions, fans tend to dislike them. However, just because they are disliked by fans does not mean that they are inherently bad. Indeed, some filler arcs such as Dragon Ball Z's Garlic Junior Arc told a story that could have easily been made part of the canon. However, there are still other filler arcs that are unimaginative, repetitive, or so outside the reasonable parameters of the story that they descend into farce.
In the Dragon Ball anime franchise, the all-time worst filler arc award goes to the Dress in Flames Arc, which makes up the last few episodes of the original Dragon Ball animated series. The arc follows Goku and ChiChi as they search for the Basho Fan that can extinguish a fire started by an earthquake that sets Ox King's palace ablaze, threatening his life as well as ChiChi's wedding dress. While the premise of a Goku and ChiChi duo mission sounds exciting, the way it's presented in the anime is utterly forgettable.
The Episode Completely Ruins Chi-Chi's Character
A better title for the arc would have been "Goku Fights While ChiChi Cheers and Cries." Unfortunately, ChiChi's inclusion adds no value to Goku's story. He just proved he's the World's best fighter in the previous story arc. Fans know he can fight. But it totally takes away from ChiChi's story. In the prior story arc, ChiChi proved she's a competent fighter who can take care of herself. She also proved she has a "tough as nails, take no guff" personality. All of these characteristics disappear from her in this arc. Moreover, the characteristic she displays contradict who she is in the manga. This arc depicts her as a damsel in constant distress that Goku must always worry about. Then there is the whole purpose of their mission. It would have been better just to focus on saving Ox King's life. The addition of also saving the wedding dress is forced and trite.
Fortunately, on the one hand, the arc was preceded by Dragon Ball's aforementioned Piccolo Junior Arc, where Goku and ChiChi participate in the 23rd World Martial Arts Tournament and ultimately defeats Piccolo. On the other hand, it was followed by the beginning of Dragon Ball Z anime, and the solid Raditz Arc. That is to say, by placing the Dress in Flames Arc between two quality story arcs, the creators lessen its impact on diluting the overall storyline. Moreover, fans that viewed are likely to forget it because Piccolo and Raditz are so much more important in and to the story. Nevertheless, it's Dragon Ball filler arc content at its worse, which is a shame considering its such a missed opportunity to develop Goku and Chi-Chi.