During the convenience store scene, as "Cash" is confronting Jack then talking to the clerk prior to leaving his silver chain moves from under his jacket to hanging over the collar and back again as the shots change.
Jack's friend has to get a triple bypass the day after the party, however he is seen at the bowling alley a short bit later in the movie, without enough days passing by to recover from such surgery, especially in the year 2000.
During the Christmas party, when Jack learns of Kate's profession, Kate eats an olive on the toothpick, however in the next shot of her the olive has reappeared, and in the shot after it is again gone.
When Jack wakes up the day after Christmas and sees Kate in the shower, she says "Tuesday's your day", implying it is Jack's turn to take the kids to winter camp and daycare. This means Christmas was on Monday and Christmas Eve was on Sunday. Jack was at the office on Christmas Eve and he told his employees in the war room there was still a full day of trading but the markets never trade on Sunday.
The color of the inspection sticker is bluish-purple. This does not match either of the current colors. Inspections due in 2001 are dark blue, while inspections due in 2002 are of lighter shade of purple than shown.
Jack and Kate used to live in the Village, yet Jack asks Annie if he had "ever taken her mother to the City". Since they moved out around the time of Annie's birth, this clearly refers to the time after that move.