There is no major differences. Only some minor changes:
- The scene where Kagami was about to wipe his collection with his sister's panties in the manga is omitted in the anime. (Where does it come from anyway?)
- In the manga, Suzune mentioned having applied for a teaching position at Higashi Shinmei high school but rejected, which is strange considering that she is a student at Ichou Academy. This part is omitted in the anime.
- The name of the magazine is changed from Nature → Nayture to avoid copyright problem.
The most major change is the introduction of the class rep as anime-original character and gives her the role of shoplifter instead of Hiiragi. Hiiragi in the anime observe him via live camera feed from her guard. Instead of giving the shoplifter a princess carry and running out of the shop in the manga, Kagami actually chases after the class rep for some distance in Akihabara in the anime. The rest of the episode is rewritten to fit the class rep into the storyline.
Since the anime airs on Sunday morning, the target audience is young children, and Hiiragi Koyomi is one of the main characters, they probably don't want to tarnish her image.
In the manga, Kagami was made redundant as a new teacher, who is a graduate from Yale university, arrives to take over the post. In the anime, he was fired due to Hiiragi spreading the image of him "molesting" a girl (the shoplifter) at the anime shop, and the new teacher (Ogami) didn't appear in the anime at all.
(Who is Tani-kan?)
The anime is lacking impact when Hiiragi Koyomi says that she wants to show the world an interesting Japan.
The professor Tim Bernard Lynn was introduced early right in chapter 3 of the manga, but her appearance and related content in chapter 3 is moved to episode 13 instead. Instead, the first half of the anime in episode 3 where Kagami was chased around Akihabara by Hiiragi's henchmen is anime original, as replacement for the scene where the professor invites Kagami to Geneva to work at CERM, but he refused, saying that he can't get signature from seiyuu in Geneva.
(Chapter 4: Getting Oshimi Mamoru to make a moe anime is difficult?)
The later half of episode 3 mostly corresponds with chapter 4, except that the anime skips a minor scene where Makina fire a teacher, and the explanation of the teacher assessment system at Ichou Academy.
Minor differences in chapter 5:
- Kagami's expression when hearing Hiiragi likes seeing Makina's reluctant expression, and his expression when asking Makina to cast magic on his French fries. In general, the anime has less of Kagami's evil expression.
- When Makina runs out of the cafe, it was balcony in the manga, but hallway in the anime. As a result, the scene where Makina shows her determination is flat and has zero impact in the anime.
- "Time to start the lecture" does not present in the manga.
- Name of the boy Makina serves: Masato (manga) → Takeshi (anime)
After the scene where Makina returns and serves the kid, the manga goes right to where Kagami had a talk with her about the prestige of a maid. In comparison, the anime added an original scene, showing the tenchou adapting herself to the taste of the customer. The other half of the prestige of a maid (the maid has to enjoy herself also), which is discussed along with the first half in the manga, is put off to the scene where Kagami shows Kiriko images of the customers thanking her.
More minor differences in chapter 6:
- The expression of Kiriko when saying "It's impossible" to singing to the crowd.
(Just notice a strange scene where Kiriko was outside the balcony, and moments later, she is inside a room with everyone else. The same thing is observed in the manga, but it is presumed that she and Makina walks back to the room when she talks abot her past)
- "Here is the other 50 point" from Kagami to Makina and the other half of prestige of a maid is discussed after Kagami shows the pictures to Kiriko instead.
- The scene where Kiriko decides to sing and walks out to the balcony is lacking impact in the anime.
- "Kyou no juugyou wa kore made" (Thus, I end my lecture for today) does not present in the manga.
Minor differences in chapter 7:
(Is the symbol behind Hiiragi Koyomi in the principal office a reference of something in real life? What is the writing above it?)
- The writing above the map and symbol in the principal office is missing in the anime.
- The conversation between Kagami and Suzune is cut short in the anime, and there is no introduction to the full view of the academy, since it is already done in episode 3. In the manga, Kagami was in the bag the whole time until he arives at the high school school gate, but in the anime, he pokes his head out in the car, so he could see the school from a distance.
- Suzune points the bat sideway in the manga, but pointing towards Nanami's face in the anime.
- Again, Suzune and Nanami's attack in the anime lacks impact.
Minor differences in chapter 8:
- "I suppose one day would have been sufficient for you" is omitted in the anime.
- The anime adds a flashback of Nanami's meeting with Hiiragi, right after the scene where Hiiragi announces that Kagami will have a battle with Nanami.
- The scene in the infirmary is shortened, and Kagami does not try to run away from the window in the anime.
(The anime also makes a reference to "The Last Leaf" by O. Henry in the scene above)
- Nixi (Mixi) is not mentioned in the anime, just SNS in general.
- In the manga, they went to a batting cage to talk about Nanami's past. In the anime, they stay in the maid cafe.
- Nanami is said to be the cause of his father's death in the manga, but in the anime, his father is said to have died of illness.
- Minako tells the whole background of Nanami in the manga, but parts of his history (esp. the scene where Hiiragi told Nanami to attend Ichou Academy because she bought him) are Nanami's flashback in the anime.
- In the anime, Kagami said "So now she's pitting her problem children against each other", which is not in the manga. In the manga, they discuss about how to stop Nanami from going violence, and Kagami said it's not interesting to do only that.
- In the anime, Suzune and Kiriko didn't tail Kagami and Minako when they went to meet Nanami to agree on the subject of the battle.
Minor differences in chapter 9:
- The anime omitted the scene showing Kagami playing the video game with extreme high score.
- In the manga, Nanami mentioned that he only has a NES. The anime omitted the brand name and only say "console".
- In the anime, Kagami didn't go home even after midnight, but the manga doesn't have such scene.
(There is an animation mistake (?) in the anime @20:52, where the screen shows score 0-0, but in the next scene, the score is 44-0)