In his free time, Anderson is a superhero (I'm thinking a Superman analogue, but whatever floats your boat), which naturally makes him sleep-deprived and distracted, and maybe it's hard for him to tell what humans can and can't see/notice. Sherlock knows he's a superhero, but doesn't see that as an excuse or even a reason for his behavior. He doesn't say anything about it because it's so obvious that it's boring--Anderson doesn't even wear a mask, for crying out loud! ...Nobody else realizes that Anderson's the superhero.

In the myth of Er, Odysseus decides to become reincarnated as an ordinary person. So...what if that ordinary person is John Watson?

Sometime before he meets John, one of sherlock's experiments goes horribly wrong and now he's a zombie. Those body parts? Not (just) for experiments. And he doesn't eat a lot of normal food because it does nothing for him. Nobody knows except Mycroft. But then, somebody finds evidence that he eats the body parts.

Sentinels are (and perhaps always have been) known to the public. John Watson awakened as a Sentinel while he was in the Army, where they take a very military approach to things (which is more than a little bit different from things for civilians); he's never experienced life as a civilian Sentinel until he's discharged. His therapist thinks his limp is because he's so traumatized by the death of his Guide. John never told anybody that he never really saw the point of a Guide, since he was so new to being a Sentinel; all of the Sentinel experts insisted that all Sentinels needed a Guide. Just because his Guide never really seemed to do a thing for him (not that the guy was incompetent or anything; he just felt the same with or without the Guide) didn't mean John knew everything. Maybe it was just a subtler effect than he'd been told that it was; after all, he'd never really had any problem with zoning, but maybe that was because he got hooked up with the Guide right away. And certainly, after he returned to London he started to have problems with zoning.

Sherlock refuses to believe that Sentinels need Guides, and from the first day sets out to prove it to John. (Either he's just a normal person or he's a Sentinel who couldn't take a normal job if he wanted to because he doesn't have a Guide...I think I prefer the normal person).

Once John is in "London is a battlefield" mode, his zoning problems disappear completely. Most people don't realize that he's a Sentinel, because he doesn't do obviously Sentinel things like zoning or having a Guide going everywhere with him. Lestrade and Co. realize, because at the first crime scene (and all subsequent ones) Sherlock has no problem ordering him to use his senses. People who do know keep taking him and Sherlock for a Sentinel/Guide pair, to which they keep going "um, no"; Sherlock doesn't have the Guide genes at all, and even if he did he'd be the worst Guide ever.

John can't get a job (at least as a doctor...nobody would care if he was trying to become a janitor or something, but there's liability involved if he zones out during something important) unless he has a Guide. John really doesn't want to put Sherlock down (and there's nobody else he can put down), but if he doesn't he won't be able to get a job. He gets really irritated at that and other ways that civilian Sentinels are treated; he has his senses under control, he doesn't need to be treated like he's going to break if he does things like a normal person. Sherlock treats him like a normal person, which is awesome even if Sherlock's usual way of treating normal people leaves something to be desired.

Sherlock is NOT John's Guide, and he's totally right about (some) Sentinels not needing a Guide.

John Watson is a hallucination/a ghost that only Sherlock can see.  People notice that he talks to thin air, but how is that any more bizarre than anything else he does?  And as time goes by, he starts to be...not more normal.  Maybe more accommodating of all of the people who aren't as brilliant as he is?