I was proud of myself for writing a relatively short critique... only to find that the crits already here are shorter yet. Sigh. I think I should just resign myself to being "the windbag" and move on.
ANYWAY. XD
So, my thoughts. I like the premise; this could be a lot of fun. But.
(You knew it was coming, didn't you?)
I'm a bit confused as to the onset of this sudden invisibility. In the first couple of pages it seems like it started to happen gradually--the dog (and the fact that the vets could see him) and the kid on the train both seem to indicate this. But instead of gradually becoming complete invisibility--as far as I can tell--all of the sudden nobody can see him anymore at all. Nothing seems to have triggered this change from occasional to complete invisibility, and whether it's a gradual or sudden onset is confused further by the narrator's reaction to his invisibility; his reactions definitely seem to suggest the "all of the sudden, no one could see me" kind of invisibility. So I think that some clarifying here would help.
There's a section near the beginning where the character goes on about how nobody notices him, and that he wishes somebody would. Initially, I assumed that the narrator was speaking in a figurative sense rather than a literal one. That can be powerful stuff in an emotional sense, but it's much more powerful if we actually see it rather than simply hearing about it through your character's internal monologue.
Now that I realize that this invisibility is actually a supernatural thing rather than a figurative one, my opinion hasn't changed. Loneliness seems to be an important aspect of his character, so you could really play with that idea of figurative invisibility (people don't notice him because he's shy, or not very charismatic, or whatever) and literal invisibility (people actually can't see him). And if this invisibility is a gradual onset rather than a sudden one, you could also ease us into the supernatural that way: scenes where one could explain his not being noticed in a mundane way and moving along towards scenes that are more obviously supernatural, like that kid on the bus. But again, if that's a direction you're interested in, we'd need to see all this to make it work.
Does nobody notice that the narrator is missing? For example, his coworkers, who aren't presumably all jerks like his boss, or his landlord, who is still getting his rent in the mail every month (and who has, presumably, noticed this dog living apparently on its own on his property). Because while you're talking about headlines, no mention of "Narrator's Name - Missing!" comes up.
The narrator mentioned above that the performance review was in another week. Did nobody notice him not coming into work for the week prior to the review itself, then?
To be honest, a lot of this feels more like a detailed outline than an actual short story. I hate to be the one spouting "rules" at you, but there is a lot of "telling" going on in terms of the emotions: the character has an internal monologue in which he discusses his thoughts. This is fine to some extent--Jones is a fairly reflective character, it seems--but it also means that his emotions aren't explored in any real depth. I think this is why I'm finding that parts of it are lacking a little necessary punch--the moment where he's considering suicide, for example, and the ending itself.
Another thing--it occurs to me that Jones doesn't ask a whole lot of questions of the CIA guy--doesn't wonder about what the catch is, or the dangers, or even if this guy is for real, or anything like that. This does seem a little bit odd, but I think it can work, if you play up Jones's desperation. A lot of that will come out if you expand some of the earlier stuff and really dig hard into Jones's emotions, and you could also play up that desperation in the last scene as well.
I did wonder about a bit about the locker room thing. It does seem a little bit... out of nowhere at first. (And yes, ick.) But I think the problem here is the same problem I've been pointing out all along--we're not getting enough of his emotions to really SEE that this makes sense for him to do. He's alone, he's desperate, and he's suddenly faced with this terrible sort of freedom that he doesn't know what to do with. Maybe he feels like there's nothing left for him but self-gratification. The point is, I think it can be made to work without seeming particularly odd--we just need a little more of him.
I haven't seen the episode of Buffy in question, so it didn't bug me at all. It could be that this story will work just fine for people who haven't seen it, and won't work at all for people who have.
I can only speak to this in the most general possible sense, since again, I haven't seen Buffy. (I know, I know. I'm a bad person. I'll get to it one day.) I don't know how different your story is from the original episode, but my thoughts are that--for me--it would take a little more than just changing the character's gender and age group to make a story truly different. Predicament, well that depends on just how different said predicament is. Personally, for me, it's one thing to borrow ideas from other places, but I would want to make sure I did something DIFFERENT with that idea.
That, of course, is my opinion. And again, it's not going to matter to anybody who hasn't seen the episode. There are some people who will likely go positively rabid on you for that sort of similarity, though. Just be aware that your story may be suceeding or failing based on whether or not the editor you send it to is a Buffy fan, rather than on its own merits.
Anyway. I'm going to be entirely honest with you--I don't think this is ready to submit yet. As Talyn and Shiver have pointed out, your writing is fine. I just think that we need to get a better understanding of Jones's character and his emotions. For that, as far as I'm concerned, we need less self-reflection from Jones and more scenes.
I really do think you have a solid start here, though. There are plenty of interesting directions in which you could take this. Good luck!