Plot hole: In "Alley Cats" 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 miidle 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.
Continuity mistake: In the poker scene at the beginning of the pilot we witness Will, Jack, Rob, and others playing cards. Shortly after Jack asks for "four cards please" watch the bottom left of the screen as a hand (presumably Will's) deals Jack a single card. In the next shot Will appears to have not dealt Jack any cards yet and when he does he gives Jack five cards, add that to the single card he gave in the previous shot and the Ace Jack kept from his original hand and we get a total of seven cards. Two more than Jack should have had if the hand was dealt correctly.
Continuity mistake: Following the argument between Will and Grace when she returns from City Hall, Karen tells Grace she "thinks it's time for a couple of blue bibbies." Watch closely as she removes the lid from the pill bottle, takes out some pills, and puts the lid back on. The scene shoots to Grace and we hear Karen shaking the closed bottle. When the scene shoots back to Karen we see that the pill bottle is open again and Karen closes it yet again.