Once again, spoilers lurk beyond this point, especially in the story-specific sections. You've been warned.
Yes, there are continuity gaps in the game. As the game starts, Taka tells us that he has a little sister who's eighteen years old. Kana has just applied to get into Futaba High School, and was successful.
However, later in the game, when the flashbacks have ended and we've caught up with the present once more, Kana has just turned sixteen when she tries to get into high school. Taka gave her an electric mouse doll / a love candle / a big dictionary for her sixteenth birthday.
I assume that the change in Kana's age at the start of the game was made by G-Collections, firmly asserting the 'morality' of the game's storyline and the legality of Kana's involvement in scenes with sexual content. Noble though this is, I've chosen to go with the original scenario: that Kana is sixteen when her six-month deadline comes up.