CJ says to her father "It's February," but the episode came in sequence before the Inauguration (which takes place on 20th January).
This episode is full of apparent mistakes because it is playing with the idea of confused time: it is in February and Toby has apparently finished with the speech, but in sequence it comes before the Inauguration; the reunion has Christmas decorations; most of the action is on a Saturday but children are going to school and the West Wing is clearly conducting weekday business. A clever meta.
After a call from the White House (at about the 40 minute mark), CJ has to leave during her speech. As she is explaining to her father the reason, she refers to him by his first name "Tal (short for Talmidge) instead of Dad.
In the season 4 episode "The Long Goodbye", supposedly set in Dayton, Ohio, C.J.'s high school reunion is held at "Horvath's Good Food", which is located just west of Chicago, Illinois.
When CJ switches places with her father and takes over driving, they pull away from "C Gallucci Realty, Inc.", which is at 1379 West Taylor Street in Chicago, Illinois. They are supposed to be in Dayton, Ohio.
In The Black Vera Wang we meet C.J's niece Hogan. C.J says "My older brothers are golf crazies" Indicating that she has more then one older brother. Yet they do not appear, they are never mentioned and there is no evidence of their existence in the home. C.J is left to deal with her fathers illness alone without and help from her "brothers"