When Buffy is fighting the "giant snake" her shoes are black flats. When she is finished talking with Giles and walking up the stairs her shoes are chunky black heels.
When Buffy cleaves the snake demon with a sword, the demon is shown injured but still intact. The next cut shows the demon suddenly cut clean in half.
Close to the end, when they're getting ready to call Machida, Tom hands the sword to Richard, and they all start saying Machida's name, and bows down. Scene cuts to Giles in the others upstairs and then cuts back down to Tom holding the sword, now in a standing position, while everybody else is kneeling.
One of the things Cordelia tells Buffy not to wear is anything black, yet when they go to the party Buffy's wearing a black dress. This is not an error made by the show or Buffy. Buffy is going to wear whatever she wishes and isn't going to yield to the dictates of Cordelia Chase.
Despite being a vampire, Angel is able to enter the fraternity house despite not being invited in by anyone living there.