Goodbye plot. See you later. This is an episode that I hardly watched the first time through. This episode isn't really plausible at all...a girl that nobody noticed so she literally turned invisible.
Now, not noticing, that's normal. Some people have a gift for blending in. Usually its intentional, however--when they want to be noticed they get noticed. There's also the camoflauge shield: a shield technique that encourages others to not notice you. I know some people who are really good at this shield, but the closer they get to you the easier it is to notice them--especially if you can sense energy. Again, however, this is something you have to spend effort on to accomplish.
We get some small hints that something is coming--Angel showing up is a big clue. He has a chat with Giles and goes on an errand to fetch a vital book that reveals yadda yadda yadda, our one glimpse of the plot and it quickly disappears.
Aha! We get a fascinating explanation here for the invisibility. It goes on the theory that our perceptions create the world. People started ignoring her, then they stopped perceiving her, and then due to the reality of the perceptions she CAN'T be seen. Throw in a bit of hellmouth energy and it might actually seem...plausible. Wow. I didn't expect that.
...Okay. At one point Buffy clears a room for Cordelia (the target of the invisible girl), and all she does is LOOK AROUND. Doesn't actually check any corners, doesn't feel around. She just glances around then leaves Cordelia to change. How does glancing determine whether or not an invisible girl is around? Not too smart here, Buffy.
Wow. Just..wow. The FBI comes in and nabs invisible girl to train and do dirty work for them. The FBI!!!! Plot hook, Joss Whedon, we have the trigger but where's the heap?? This hasn't been mentioned yet. If you pull the trigger there has to be a heap! Still No mention. Maybe the network's lawyers thought it would be too risky? Potential legal problems? We may never know.
Tune in tomorrow for the 'exciting' conclusion to season 1!!