Continuity mistake: Barney blocks Ted's path by standing in front of the door. Watch his position as he says, "Ted, don't do this" for the second time, he has his right arm over his head. When the camera changes angles he has it down.
Continuity mistake: In the scene at the hotel bar, the red straws lying on the table next to Ted change position between shots without being touched.
Continuity mistake: In the scene at the bar where Robin is describing looking after Marshall as being like having a baby, Barney's drink moves from in his hands to on the table and back again instantly between shots. (00:06:30)
Life Among the Gorillas - S1-E17
Continuity mistake: At the karaoke bar, when Marshall is deciding which song to sing, his beer bottle keeps switching hands between shots.

Continuity mistake: When Robin and Barney meet up for drinks, the amount of ash on the end of Barney's cigar goes up and down frequently between shots. (00:06:10)

Continuity mistake: When Lily drops the potato chips on top of the 'salad', we can see a few chips sticking up beyond the top of the bowl. The shot changes and now the chips are laid flat, with none sticking up over the top. (00:07:40)

Continuity mistake: When Robin is talking to her boss about his dog, the pens and pencils in the holder on his desk change depending on the camera angle.

Continuity mistake: When Barney is crouched down, leaning against Robin's chair, the money in his right hand vanishes between shots.
Continuity mistake: In the opening scene at the bar, when Ted is debating whether or not to ask out Robin, Marshall's beer is in his hand when the camera is on him, but on the table when the shot is from behind him. (00:03:00)
The Chain Of Screaming - S3-E15
Continuity mistake: The ice cream Robin's eating in Ted's car keeps changing shapes between shots.

Continuity mistake: After Natalie throws spaghetti at Ted, the amount and position of the spaghetti pieces changes instantly between shots.
Intervention - S4-E4
Continuity mistake: In this episode we see that Barney punched a hole in the wall next to the door because Ted broke apart a girl fight. It is supposed to be under the calendar on the right side of the door. It is also said that Ted and Robin were dating at this time. But earlier, in the episode "Wait For It..." (3-1) We see Ted going through his break up phase after Robin. One of the phases is painting the apartment, and there is no hole.
Continuity mistake: When Ted, Barney and their dates are in the tub, Barney is holding a bottle. He takes a sip (i.e. no cap) and hands it to Amy (Ted's date). Now it has a cap. She hands it to Ted who unscrews it and has a drink.
First Time In New York - S2-E12
Continuity mistake: When Robin is talking to her sister Katie in the Empire State Building lobby, Katie's bag moves between shots. Sometimes she wears it with the strap hanging straight down from her shoulder, in other shots the strap goes across her chest like a messenger bag.
How Lily Stole Christmas - S2-E11
Continuity mistake: When Ted, Robin and Barney are at the bar, discussing the fact that Barney is ill, the level of the drink in Robin's glass goes up and down between shots.

Continuity mistake: When the gang are discussing what Ted should say to break up with Natalie, the amount of beer in Marshall's glass goes up and down between shots.
Continuity mistake: The scenes before Robin and Barney leave the diner vary depending on the angle. From outside we see that Robin fixes Barney's suit before they leave, but from the inside she doesn't.
Continuity mistake: When Barney and Abby are lying in bed after the Local Art Cafe scene, Abby's arms/hands change positions between shots.
Continuity mistake: When Robin and Lily are talking in the apartment of Barney's date, Lily's hand moves instantly between shots from resting on her shoulder, to resting on the handbag by her side.
Good Crazy - S7-E22
Continuity mistake: When Ted is on a date with the 2nd girl you can see her tattoos but when Ted sees Robin the tattoos change. (00:09:50)
Suggested correction: Depending on the location settings on his laptop, they could be giving a false reading. My laptop shows I'm in Cardiff Wales while in fact I'm nowhere near.
Ssiscool ★
The show was actually filmed on a film set in Los Angeles which is probably why the laptop says Los Angeles as the current location. This most probably slipped past the editing crew.