Errores

In Episode 3, (Kendo girl in Love? - Swordplay) Motoko shoots Keitaro into the air with her sword, and Keitaro bounces on a roof, landing on his back on the floor, which is clearly intact at the time of the fall. But, in the next shot, Keitaro is laying face down, and the floor boards are boken around him and smoking.

Naru's need for her glasses varies dramatically between episodes. For most of the series she goes without them and has no difficulty at all (and there is no evidence that she uses contact lenses). And during the fireworks display at the festival, she is able to recognize Keitaro without her glasses in the dark, from behind. But earlier, when she and Keitaro both run off and break their glasses, she cannot recognize him without them even at a distance of inches.

Haruka and Keitaro both refer to the same woman as their grandmother, yet Haruka is Keitaro's aunt. This would make Haruka and Keitaro cousins, not aunt and nephew. In fact, they are cousins. Haruka's parents died in an accident and she was adopted by her grandmother; that's why Keitaro calls her aunt. (This is not explained in the series, though.) Additionally, it is common usage in Japanese to refer to an older (but not elderly) woman with whom you are familiar as "aunt" regardless of your actual blood relation to her; similarly, elderly women are respectfully referred to as "grandmother" regardless of blood relationship or lack thereof.