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.
YMMV: Ah! My Goddess
Adaptation Displacement: The TV series seems to be much more well-known amongst fans than than the manga, OVA, or movie, at least in the U.S. In Mexico and Latin America, the manga and the OVAs are this instead, because the TV series was never broadcasted there.
Sort of. Some fans are convinced that when Keiichi and Belldandy do something to signify their love (whatever that may be), the manga will end. They haven't, and it hasn't, after 23 years. However, since the two of them are extremely close as they currently are, the two consummating their love (by way of dating, making love, or even getting married) probably wouldn't make a major difference in the tone and flow of the series, which why it's "Sort of". It should also be noted that in the OVA, and in the manga prior to the Lord of Terror arc, they had a very close relationship (even though Keiichi still couldn't spit it out).
Even if you disregard Keiichi and Belldandy's relationship (or accept it as a Foregone Conclusion), there's still the issue of the fact that the manga is published monthly, and since the Mystery Child arc, Fujishima seems to be slowing down considerably, taking much longer than needed to write a story (the Lind Arc is truly epic, but does a broom race between Belldandy and Hild really need five chapters?)
Evil Is Sexy: Hild, anyone? Mara and Hagall definitely fit the bill as well.
Fashion-Victim Villain: The punkrock outfits the various demonesses wear are certifiably fabulous! Especially those of the more powerful ones. Also qualifies for Costume Porn.
Faux Symbolism: Urd is basically the daughter of the Almighty and the devil. Or rather, her mother is Hild, the ruler of Hell, and while it is debatable whether it is stated outright, it is at least heavily implied that her father is God The Almighty.
Well, in the OVA at least, Belldandy's father is The Almighty. But then, the OVA doesn't precisely follow the canon of the original manga.
It's now been confirmed in the manga that the Norns' father is in fact The Almighty.
"Funny Aneurysm" Moment/Harsher in Hindsight: Many people, both in universe and in the fandom, make fun of or complain that Keichi and Belldandy are not that intimate despite being the Official Couple and being together for years, decades in Real Life. Then came the revealed that the reason why is because Heaven was suppressing Keichi's urges towards her because inter-species romances was forbidden.
Or in Belldandy's case, "Growing The Ponytail". It took Fujishima a while to get a handle of the character designs, but when the goddesses start taking on a less Oriental look in the manga, the manga starts developing into the light-hearted romantic comedy it's best known for.
This might be why the OVA (which debuted while the series was still Growing the Beard) and the TV series (which debuted well after the manga established itself as a light-hearted romance), both of which seem to be more popular among fans, have Belldandy make her first appearance with blonde hair in a ponytail, and wearing the blue, gold, and white goddess outfit she's frequently associated with (which fans agree she looks more attractive in anyway, as opposed to loose, silver hair and the... thing... she wore in the manga's very first chapter).
Les Yay: Boatloads in the manga, typically in a Not What It Looks Like context. For instance, Urd pressing her open mouth to Belldandy's... to suck out an "Ahem Bug" causing laryngitis. Seeing her do this paralyzed Keiichi.
More recently, Urd briefly messed with Peorth's head by pretending an accidentally swallowed potion had made her fall in love with Peorth.
There also a scene where Belldandy was seen in a liplock with Peorth, doing the magical equivalent of CPR, which of course looks wrong and actually freaks Peorth out. The reason? Belldandy was trying to suck a water spirit out of Peorth's body.
Sayoko and several other girls were clearly thinking Les Yay in an early manga chapter when Urd hooked a finger into the top of Sayoko's swimsuit and pulled it open to take a good look inside. But...
Some fans see Foe Romance Subtext between Urd and Mara. It gets better when a clone of Urd is threatening to destroy Urd, and Mara shouts, "I can't lose you! I still haven't beaten you at Tetris yet, dammit!"
Mara getting mistaken for a pervert is a repeat gag in the anime, with both Sayoko and Megumi thinking she's after them for sex (when actually she wants a minion and to possess Megumi's body, respectively).
For some (especially on /a/, Belldandy of all people after Chapter 285. See "Funny Aneurysm" Moment above. Yes, it was the elites of Heaven who were ultimately responsible for sealing Keiichi's libido, but having Bell say that she liked being pampered by him without any sexual pressure rubbed a lot of fans the wrong way (as well as opened upa pretty ugly can of worms).
Uncanny Valley: The manga went through a Dork Age of sorts (between around volumes 27-33) where the characters' eyes were usually drawn without reflections, and their noses were reduced to a pair of nostrils when seen from the front, giving them a disturbing dead-fish look. Thankfully, It Gets Better.
Villain Decay: Mara got hit by this trope hard in Flights of Fancy. When she first appeared in the first season, she could easily give Belldandy and Urd a hard time by herself. Suddenly, she's working at the convenience store Keiichi and Belldandy used to work at (they gave her the job), lives in a rundown building (though, an abandoned arcade was her base of operations in the manga), sleeps alongside her rat scientists, and eats nothing but takeout food from the store she works at. She can't even get into Tariki Hongan Temple to cause any trouble because Banpei can dispatch her easily. Urd even points out how big a failure Mara is, causing her to break down and cry. Really, how can you not wonder where her badassery went and pity her at this point?
The Woobie: Sora when she explains why she thinks◊ she's◊ a jinx◊. Go on; tell me you don't feel like giving her a comforting hug. (Note: these translations were flipflopped; read left to right.)
The Goddess of the lake; when she was still human, her village was in a terrible drought in which she chose to be sacrifice to restore it. After becoming a goddess, she can never leave the village all the while many of the villagers left over the years.
Second episode of the TV series dub, Keiichi tries to stay at a friend's house during their mah-jongg game— and keeps on winning due to Belldandy's presence. He aptly exclaims, "Well, luck be a goddess tonight!"