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This is the first of two OVA episodes released directly to DVD in the Japanese original, which consist of small side stories as a bonus. This particular episode is based on chapter 42 of the manga.
For the original backstory, this event in the manga does take place after the Lord of Terror arc, but Urd's episode originally took place after Skuld's story. They also shifted the focus of this episode to be entirely on Urd, rather than following Keiichi and how he went about to make the moonstone (who cares? Urd's more important, anyway).
The beginning of this episode begins with a small event from chapter 40, where Belldandy fixes the house from the Lord of Terror incident. Originally, it took two chapters until the effects of Yggdrasil's crash were visible on the goddesses. As far as I know, in the original manga, Belldandy just fixed Tarikihongan, not all of Nekomi.
Urd's license was never really reinstated in the manga, unlike the anime. After the Lord of Terror arc, all contracts and suspensions couldn't be carried out due to Yggdrasil's crash, but apparently they still have a way of keeping those records.
Originally, Urd and Skuld regressed and progressed in age at the same time. The explanation that Skuld is currently unaffected due to her lack of goddess power is new to the anime. The explanations for the power sources and such are a bit condensed, but otherwise unchanged. And Chibi-Belldandy appeared mighty fast in the anime.
As I've stated before, the story of how they got the alternative energy source is more or less only touched upon and ignored. Originally, Keiichi and Belldandy received a message from Kami-sama through a fortune teller that moon rocks could be used as an alternative energy source. This is what brings Skuld back to her regular age, but when they tried it on Urd it was only partially effective enough to make her an older child rather than a toddler. Then they found out that moon rocks were igneous (molten from a volcano), so they did that and that's when Urd became an adult again and kissed Shohei goodbye.
Urd's statement of her parents taking a hands-off approach is new, and hilarious... especially considering her indifference towards her father and her unwillingness to love her mother.
Originally, Urd and Shohei met while she was wandering the streets right after she got her new clothes (and the first moonstone attempt), and she collapses when she asks Shohei to buy her sake. He forfeits buying a video game (for the Turbo Grafix, which pwns the PSP) for her sake, and that's when she shows her a bunch of video games.
As an interesting side note, this is the first part of the manga where the waviness of Urd's hair emerges.
Originally it seemed that Urd didn't have much knowledge of videogames. I guess she keeps up with gaming news in the anime. Then again, she does play Tetris...
The sake bottle is new. Well, Urd leaving it for Shohei to keep.
Urd surprising Shohei like that is the same. But thew new sake vending machine scene and Shohei's hesitation are all new, though. Basically, they move right to the construction site scene.
Originally, we never heard Urd sing until the Hild arc, volume 22.
Awww, they removed Urd's "life's more fun when there's an edge to it" line. Bummer. The restatement of the sake is new as well, though.
Urd didn't have doubts about being too involved until she found out Shohei followed her in the manga. And in the manga, she never told Shohei that she wasn't a child.
Originally, Urd removed her clothes because she didn't want to ruin them. I guess that's too risque for DVD.
Again, the bloody sake bottle. Honestly. But at least Shohei got some character developement for a one-shot character. Originally in the manga it was pretty certain that they wouldn't meet again, but it seems like in the anime they want to keep the possibility open.
Overall, I did like this episode a lot, and believe it be well done... possibly even an improvement over the manga, much like the Lord of Terror arc.