Plot hole: Spike must have had his chip implanted while he was unconcious. If so, how did he attack The Initiative scientists without any pain when he tried to escape? You could argue that they programmed him to be capable of violence within The Initiative only, but why would super smart scientists program an evil being to be able to escape at the first opportunity? Joss Whedon has acknowledged this as an oversight.
Plot hole: Willow hacks into The Initiative's computer system and discovers air ducts and electrical conduits leading to Adam behind 314, but the room doesn't show up on the schematic. It seems unlikely that nobody who didn't know about Adam would have noticed this and investigated.