After getting denied access to his apartment complex by Tony because he's not recognized, Jack drives to his office building. As he walks in through the revolving doors, Jack accidentally hits his head on the glass and ends up touching the spot that he bumped but continues with the scene.
Near the end when Jack stops by Kate's apartment and she is moving out, Kate's assistant complains about working on Sunday. Kate says the assistant hadn't seemed to mind when she opened the pot of bag Kate bought her.
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.
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.
Kate complains about Jack's potential commute from Teaneck to Wall Street. But, depending on traffic, it's as little as 20-30 minutes, as evidenced near the end of the film when Jack says he'll be in the office in 20 minutes.
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.
Annie tells Jack that alternate-Jack had a star named for Kate as an anniversary gift. The star names recognized and used by scientists are those that have been published by astronomers at credible scientific institutions. The International Astronomical Union (the worldwide federation of astronomical societies) accepts and uses only those names. Such names are never sold. While it's not completely impossible that Jack managed to convince them to name one after her, it's exceedingly unlikely.
When Jack sees Kate after the glimpse has ended (as she packs to move), she has a very distinct hair cut. Just a few hours later when Jack confronts her at the airport (and they eventually go for coffee), her cut is a completely different style, much more similar to Kate from the glimpse.
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.