Continuity mistake: Kirk did not know who Miss Patty was. He said "I wasn't aware that you were THE Miss Patty." Later in the series, in Episode 5 of Season 6, at Miss Patty's Grand Recital, Miss Patty introduces Kirk's performance and says that he was "a talented pupil of mine". His performance was titled, "20 Years Ago Today", therefore Kirk was a student and should have known who Miss Patty was all along.
Visible crew/equipment: After Rory tells Lorelai that she looks happy, when it cuts to Max telling his class about Emily Dickinson's poem, we can see the boom mic bobbing around at the top of the screen. (00:07:55)
Continuity mistake: After Rory is walking with Dean, it goes to a shot of Rory and Lorelai eating at Luke's Diner from outside. Rory is wearing a light blue sweater and Lorelai has a black shirt on. Then it goes inside the diner and Rory is wearing a dark bluish/grey sweater and Lorelai is wearing a purple shirt. The first exterior shot is used from the very last scene of the episode. (00:27:05)
Other mistake: Rory asks Emily for baby pictures of Lorelai, but Emily says Lorelai burned them all because she had such a big head when she was little. But in "Love and War and Snow" earlier in the season, Emily, Richard and Rory looked at a baby picture of Lorelai in a bunch of petticoats the night Rory stayed over with her grandparents during a snowstorm.
Continuity mistake: In S1E3 "Kill Me Now" when Babette tells Lorelai that Cinnamon is stuck under the porch again, she refers to Cinnamon as "him", but in this episode Babette talks about Cinnamon being female.
Continuity mistake: When Lorelai and Max are on the porch talking about whether or not Max can go in, there are a few snowflakes on Lorelai's hat which disappear and reappear while they're talking.
Double Date - S1-E12
Factual error: Lane wants Rory to talk to Dean about setting up Lane with his friend Todd. While asking Rory to do this, Lane asks for the date to be planned for the following Sunday, after church; however, Lane is Seventh-day Adventist and they believe the Sabbath is Saturday and therefore attend church on Saturday, not Sunday. (00:04:45)
Suggested correction: Many Seventh-Day Adventist churches do actually hold church on Sunday.
Kill Me Now - S1-E3
Audio problem: When Lorelai and Rory are sitting at a table, with Rory looking at herself in a mirror, they talk about Rory's hair. Right after this, Rory asks, "do you want something to drink?" Her mouth doesn't move at all. (00:30:00)
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: Luke uses a red screwdriver trying to get something out of the toaster and leaves the screwdriver in the toaster while he goes to get coffee. When it cuts back to Lorelai, the screwdriver is on the counter, beside the toaster. (00:18:20)
Continuity mistake: During the town meeting, when Harry is talking about the Battle of Stars Hollow, in the shots facing Harry his hat is sitting on the top edge of the lectern, but in the shots from over Harry's shoulder the hat is sitting on the lectern's inner shelf. (00:01:15)
Forgiveness and Stuff - S1-E10
Visible crew/equipment: After Richard is brought to his hospital room, when Luke tells Lorelai that she's avoiding seeing her father, the boom mic dips into view at the top pf the screen when she says, "You know what hurts? A screwdriver in your head." (00:30:25)
Factual error: When Rory drives up the road, in the shot from inside the car there's a stop sign facing her up ahead to her right, but in the next shot that stop sign is now facing the opposite way, which has the wrong side facing the driver.
Visible crew/equipment: When Lorelai and Rory are trying to get to Luke's they wind up in the alley, and in the next shot inside Luke's we can see the reflection of the moving camera on the glass door, behind the guy wearing a blue check flannel vest. (00:11:50)
Continuity mistake: When Babette walks through the kitchen's back door to comfort Rory, the porch is visible with its lattice wall and doorknob is to the right, but when Lorelai walks out with Babette in the exterior shot the wall has changed and the doorknob is to the left. The exterior shot looks like the area outside the side living room door, not the kitchen door. (00:19:00)
Visible crew/equipment: When Lorelai takes the ice bucket into the kitchen trying to evade Emily's questions about Luke, just as Emily tells her that Luke is always around when Lorelai's in trouble, on the glass cabinet there's a visible reflection of the boom operator moving around, while holding the boom. (00:39:10)
Continuity mistake: After Dean kisses Rory the second time, when Rory joins Lorelai in her bedroom the lamp sits atop a simple rectangular box to the left of the bed, but in the following shots there's a round table with a pretty table topper and frames, etc. beside the bed. (00:42:00)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Richard is sitting on the porch and Rory brings him a Cosmo magazine with a quiz, the shadow of the boom mic dips down over Richard's head, at the top of the screen. (00:37:05)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Emily and Richard are in the car, Emily tells him that Lorelai's right about not knowing her at all, and when it cuts to Sookie and Lorelai in the kitchen, lighting equipment is visible at the right side of the screen. (00:42:10)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Rory is cutting her cake the doorbell rings, and in the shot of Emily and Richard the lighting equipment is visible at the left side of the screen (it's not there in previous and following shots). (00:33:35)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Rory shows up at Luke's to meet Lorelai, just as Lorelai says, "Nice face you got on there," we can see lighting equipment at the top left side of the screen. Then, when Luke brings them coffee it's visible in the shots from the same angle. (00:11:30)
Suggested correction: That's exactly the point of the scene. Kirk knew that her name was "Miss Patty" but he didn't know she was THE "Miss Patty" about whom everyone was speaking.
They also refer multiple times to Kirk growing up in Stars Hollow. He would have known. In Stars Hollow, there couldn't ever be another "Miss Patty." That's just not how they roll.