Plot hole: Ellen and Rob wear wedding rings, yet their wedding is not announced until "An Affair to Forget" in the second season.
Plot hole: The apartment block where Will lives supposedly has the same layout for each floor of the building. Yet in "Yours, Mine or Ours" the room 12D is seen as located right in front of the elevator, the same location as Will's apartment door - however Will's apartment is always seen as 9C.
Alley Cats - S1-E21
Plot hole: When they are bowling and Grace is losing, she says she's fine with it and she knows how it feels to be her middle sister, then Will reminds her that she's actually, "The baby of the family looking for Daddy's approval." However, in all later episodes, Grace is portrayed as the middle child with a younger sister, Joyce and an older one called Janice. This mistake is made in a few other places through the show, where Grace either refers to how old she is (youngest, middle child etc) incorrectly.
Alley Cats - S1-E21
Plot hole: In the bowling alley scene, Ellen states that Grace would need to knock down 27 pins in order to tie. Will and Grace then have a conversation, and Grace gets a strike with her next ball. They then start gloating that they have beaten Rob and Ellen, but the scores don't add up, and they couldn't go into the lead on that round.