Deliberate mistake: When Willow and Jenny go out to the parking lot only to discover vampires converging on the school, pay attention to the extras. You can make out some of the same extras in different shots coming from different directions. (Most notably, you can see a woman in a long black-and-white skirt coming from the direction of the parking lot, then a few shots later, she's suddenly over in the football field coming from there.) They obviously reused extras in different shots to "pad out" the crowds.
Never Kill A Boy On The First Date - S1-E5
Deliberate mistake: When Buffy and Giles are searching the funeral home, we see three shots of Buffy and Giles opening up different mortuary-cabinet doors, shot from the point of view of the cabinet. The problem? You can tell they're opening and closing the same door over and over again. The background is exactly the same, and all they've done is slightly re-arrange the stuff behind them, and had the actors come in from different angles to create the illusion they're opening different doors. It's SUPER obvious.
Deliberate mistake: When Xander ducks under the caution tape to catch up to the group of students at the beginning, as the shot is about to cut, judging by his casual walking pace, he should maybe be 10 or so feet ahead of Buffy and Willow. When the camera cuts, he's suddenly at least 30 feet away. It's probably edited that way for time reasons (to quicken the pace of the scene rather than show him walking an extra 10 seconds), but still a minor mistake.
Deliberate mistake: When Willow goes into her dark bedroom, she turns on her lamp. Somehow, her tiny lamp illuminates the entire room and also casts a shadow behind her, even though it's behind her. Clearly, when she turns on the lamp, they also turned on some set-lights in front of her to make the room bright enough for filming. There's also something else that gives it away-when she turns on the lamp, the studio lights come on a split-second later - just enough that if you look closely, you'll notice the delay.
Deliberate mistake: When Buffy, Xander and Giles try to "delete" Moloch from the computer, watch the computer screen as she sits down. There's already a folder labeled "Willow" on the desktop. Buffy then types in the word "Willow" to search for the document (without clicking on any sort of search bar, so typing it would do nothing), then says something along the lines of "That's probably it" and proceeds to click on the "Willow" folder... that was already on the desktop. The entire scene makes no sense.
Chosen answer: Angel is saying that he is still jealous and Buffy recognizes that this is his way of saying he wishes that they could be together. That is why they both smile.