When Riley and Buffy are about to have sex, when Buffy lies down, the bedding and pillows are charcoal and cream striped. A few shots later, the sheets and pillows are dark red. The reason for this (which one can see when looking closely) is that the striped bedding and pillows are the duvet and shams, and the red sheets are underneath. As time progressed, the duvet and shams were tossed aside, leaving only the red sheets and pillows.
During the slow-motion fight with the Polgara demon, both Riley's telescopic baton and the Polgara demon's deadly arm skewer bounce and wobble as if made of foam rubber, or some other soft material. These were most likely stunt props.
It makes no sense for the Initiative operatives to shoot Spike with a tracer. They want to capture him, not trace his movements. The logical thing would have been to shoot him with a tranquilizer dart.
(at around 34 mins) The boom mic can be seen above Buffy as she is asking a question.
When being integrated into the Initiative, Professor Walsh hands a pager to Buffy. Buffy then insinuates that she has never had one before and that she has meant to get one. However, Never Kill a Boy on the First Date (1997), when she is about to go on her date with Owen she says to Giles "If the apocalypse comes, beep me." as she holds up a pager.