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.
Plot hole: Will and Jack are out on the patio talking about the first time they met at a party (implying in college) and how Jack convinced Will to come out, but in S1E6 Jack talks about Will's favorite book in elementary school. I am re-watching the show now, and I am sure they have a conversation about hanging out as kids. Makes no sense. Time 1 is season 1 and time 2 is for Season 2. (00:06:33 - 00:13:10)
Suggested correction: I just re-watched the scene you referenced from Season 1. Jack is talking to Grace and is throwing out random Will trivia. He never said he knew Will in elementary school, just that he knows what Will's favorite book was when he was in elementary school. There is no plot hole with this statement.
Lows in the Mid-Eighties (1) - S3-E8
Plot hole: In this episode during the flashback scenes, it is shown to us that Will comes out of the closet during his freshmen year of college during Thanksgiving Break, when they spend the weekend at Grace's Parents house. However in the season 1 episode "William, Tell" Grace claims that Will came out to her at senior year of college during Christmas Break. Quite a difference for such a memorable time.
Fred Astaire & Ginger Chicken - S6-E20
Plot hole: Jack spends part of this episode clumsily teaching Karen basic steps of the fox trot for her wedding dance with Finster. However, in season 4, episode 16 ("A Chorus Lie") It is established that Karen and her husband Stan have, for years, performed an annual spotlight dance at their Valentine's party on Shelter Island. Later, she and Will are seen beginning a rather elegant fox trot to "Someone to Watch Over Me," complete with spins and a dip.
Plot hole: The whole Series 7, episode 5 "Key Party" revolves around Will's 37th birthday. Yet in Series 8, Episode 2 ("I Second That Emotion") Will is talking with Karen at the bar and says "I'm unemployed, I'm single and I'm 41", and four years certainly didn't pass.