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.
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.
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Lorelai gets home while Rory is on the phone, just as Lorelai jokes about Justin and Britney, filming equipment is visible at the left side of the screen. (00:06:35)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: At Chilton, when Rory walks past the girls talking about another obligation party, in the next shot facing Rory we can see lighting equipment at the right side of the screen. (00:08:20)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: After Rory takes Tristan's invitation and walks away, when it cuts to Emily and Lorelai shopping at Damion's, just as Emily notices the hat we can see the crew member and equipment at the right side of the screen. Then, when Emily finds the light-up bracelets and shows Lorelai, some lighting equipment is visible at the left side of the screen and cables are on the floor behind them. (00:08:30)
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)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: While Emily is instructing the servants before the party, when she tells one servant, "I want those six inches apart, get a ruler," there are two problems with this medium shot. First, lighting equipment is visible at the top right side of the screen over the lamp, and second, it's a flipped shot. Note the painting and lamp are reversed in the medium shot, compared to the next wideshot which is fine. (00:17:45)
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 Lorelai walks into the kitchen and tells Sookie that Emily and Richard have shown up, during their conversation the lighting equipment is visible at the right side of the screen, in four shots facing Lorelai. (00:34:55)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Emily raves about Sookie's hors d'oeuvres, the shadow of the boom mic is bobbing around at the top of the screen. (00:35:10)
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: As Lorelei climbs into bed with Rory at 4:03 there is what appears to an open book being lowered out of the shot by a presumed crew member.
Rory's Birthday Parties - S1-E6
Continuity mistake: Rory's piece of birthday coffee cake changes sizes throughout the whole scene.
Rory's Birthday Parties - S1-E6
Continuity mistake: Lorelai is on the phone with Emily talking about shopping. The apple she is eating changes places with each shot.
Continuity mistake: While Rory is at Doose's, when Dean surprises Rory and kisses her, in the first shot facing Dean his head is leaning to his left, but in the next shot Dean's head is now suddenly leaning to his right. (00:04:30)
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)
Visible crew/equipment: In the last shot, when Rory starts telling Lorelai all about the market kiss with Dean, some lighting equipment becomes visible at the right side of the screen, as the camera pulls back. (00:43:20)
Continuity mistake: Luke is at a table talking to Miss Patty while Lorelai stares out the window at Rory and Lane. Except behind Lorelai you can see Luke at the register alone, even though his voice is still heard talking to Miss Patty.
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)
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.