On Keitaro's arrival at the Hinata apartments, Shinobu is already a resident in the manga, but in the anime she doesn't become a resident until episode 2. Motoko is present at the apartments in the Manga. In the anime she has gone away on a retreat and doesn't return until episode 3. These differences introduce characters one at a time, perhaps because this less confusing in an anime than introducing them all at once.
In the Anime, Granny Hina phones to ask Keitaro to visit her, but then she goes off on a trip before he arrives. In the Manga he goes to visit her on his own volition, unaware that she went off on a world tour a year earlier. Also, in the anime, Granny just makes Keitaro the manager of the apartments. In the Manga she signs over the deeds of the property to him, making him the new owner.
In both the Anime and Manga, Naru is the first one of the residents to learn that Keitaro is not a Tokyo University student, and in both occasions she tries to hide it to help Keitaro. However, the situations under she learns it is different. In the Manga, she asks Keitaro about a dish in the Tokyo University restaurant, knowing the dish doesn't exist. In the Anime, she learns it through Keitaro's grades.
Certain characters are anime-only. These include Kentaro, the automaton Moe, the Hinata Elders, and Naru's sister Mei. (Mei is mentioned in the Manga, but doesn't actually appear until the end of volume 14 and even then only briefly, appearing in only one chapter and with no dialogue).
When Keitaro and Naru go on their journey of healing and self-discovery to Kyoto, they don't recognize one another at first because neither is wearing glasses. However, in the Manga they soon come to put on their glasses. They try to separate but keep meeting, seemingly by coincidence. In the anime their glasses get broken, and they don't recognize each other until the glasses have been repaired.
The first photograph with a girl on Keitaro's photo album takes place in Kyoto in the Anime, with Keitaro being unaware of the girl being Naru until they wore their glasses. In the manga, the scene occurs much earlier, when his identity as a ronin was revealed and he was about to leave the dormitory for good. In this case, he was aware of Naru's identity.
In the Anime, they meet Mutsumi at Kyoto railway station. Keitaro has already bumped into her once, prior to the exams, and that is how he knows her name. In the manga they meet her on a ferry, having left Kyoto.
The anime does not cover the whole of the storyline presented in the Manga. Because of this, Ema Maeda, who appears only in the last volume of the Manga, is not present in the anime.
Some episodes of the anime do not correspond to anything in the manga. These tend not to advance the storyline, so they could be regarded as filler, but they do help to bring out some details of the characters.