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This episode is based off of manga chapter 40. They went ahead and skipped a lot of chapters, and it looks like they'll be skipping even more because the following chapters deal with the direct aftermath of the Lord of Terror Arc, which was skipped.
The manga originally began with Belldandy rebuilding the house with her power (due to it being crushed by the Lord of Terror), and then Skuld offering to fix up Keiichi's motorcycle because she used it for one of her crazy inventions in the preceding fiasco. This was obviously left out and altered, due to the fact that they skipped the Lord of Terror arc for this time.
Skuld's character seems to have regressed a little bit from her debut episode last week. However, in her defense, the manga moved right to the Lord of Terror arc after her initial appearance, thus not giving much chance to show off her immaturity until much later. So, this episode's opening of Skuld latching onto Belldandy is something, I guess, akin to a backstory. Belldandy was the one largely responsible for raising Skuld, and given Belldandy's nature, it's only a bit natural that Skuld would want to be spoiled a little.
So, it's only natural also that Skuld would be appalled that Belldandy would have to go to this thing called "school" with Keiichi, and that Skuld would want to wreck apart the motorcycle. Also, given Skuld's quirkiness, it's only natural she'd begin to start "improving" the bike rather than tearing it apart.
Megumi originally came over to Tarikihongan because Keiichi's phone was out of commission due to the Lord of Terror incident, not because she had some free food she wanted to be cooked. Skuld's impression of Megumi was kept more or less the same... and so was how Keiichi took off on it.
I still think Belldandy telling Skuld to issue an official challenge is way too funny. Tamiya and Otaki's entrance is kept the same.
The fantasy of the Robot Wars was kept. Wow, that was funny. Seriously. "Don't look into other peoples' minds without permission!"
The discussion about the rules is extended. Originally, it only covered that you get drums of oil; harming your opponent's robot isn't mentioned, but it wasn't stopped later either.
The scene at the college was kept, and was even funnier in animation in my opinion. Skuld mentioning that humans are ill-mannered (which a good amount of us are) is new, and so are the raw materials presentation and such. The manga goes directly to a short scene on how the robots are built, then immediately into the robot battle.
The anime delves into the actual production of the robots a lot more. This episode also touches on something that is heavily emphasized in Eastern culture, and that's teamwork and community over individuality. Even Skuld's sisters and Keiichi see this, and help out Skuld behind the scenes in the anime.
In Megumi's words, "there's only so much you can accomplish by yourself."
In DH's release, Belldandy says, with a cheerful attitude, "Skuld's such a stubborn child... but I'm sure she sees a little of herself in Megumi. And at the same time, something completely different,too. I hope she can find both in her life. Don't worry, Keiichi. In the end, they'll be good friends." In the anime, Belldandy is more concerned than that, and feels a little guilty for making Skuld do this. Keiichi's the pessimistic one in the manga, and now the optimistic one in the anime.
Urd's comment, "She's absorbed in the joy of making something" is something that defines Skuld's quirkiness. That's the reason Skuld improved Keiichi's motorcycle, and also why in the Lord of Terror arc she went happily forging the ten-dimensional scythe.
Megumi referring to Skuld's robot in terms of the motorcycle before is new to the anime. The robot battle basically consisted of, in the manga, Skuld showing off the destructive capability of her robot, then Megumi realizing she can trap Skuld's robot, then doing so.
That's another important part of Skuld's early personality... She gets so caught up in the end, she ignores the means (opposite of Urd). So, while her machines get the end done, they often scew up because Skuld's lost sight of everything else.
The self-destruct's the same. The bet-money fiasco's the same. The shock handshake's the same. I'm wondering if there's any special meaning in showing the Star of Misfortune at the end...?
Looks like next episode is going to introduce Banpei.