This story is not yet complete, but it seems that the sick boy serves as a vehicle for the larger issue of establishing connections between the Muggle and Magical worlds in law enforcement and medicine.
In the attention-grabbing beginning to this story, the Constable is looking for the "mystery man" who has left such a meager paper trail in his life. We catch a glimpse of the Dursleys, Petunia who has softened in her attitude toward Harry, and Vernon who is as irascible as ever. And we see Robert's first interaction with the wizard Harry.
It is a little hard to accept that Harry decides to confide everything in Robert so rapidly, or that Robert believes in Harry's magic world so quickly. Even given the incentive of helping a dangerously ill boy, one might expect more caution in Harry or more skepticism in Robert, and later in Eleanor. Still, Chapter 1 is interesting and enjoyable, and the sentences are well constructed.
Chapter 2 had two little issues for me. First, a lot of magical characters (Ginny, Ron, Hermione, Neville, Hannah, Madam Pomfrey, Kingsley, and the kids) are introduced all at once. I get a feeling of a Class Reunion. It seems overwhelming. I might have introduced them more slowly, one or two at a time over the rest of the story.
The second issue is that in-jokes and obscure references (such as trout and mushrooms) in the presence of Muggles who don't understand them and therefore get confused and cannot follow the conversation are not polite. I have seen this in other works of other authors, and it seems out of character for Harry and his friends to behave that way in front of their guests. It feels exclusionary. On the other hand, Hermione's impulse to explain Gamp's Law is the opposite; she is trying to be inclusive, though Ron's brief explanation ("rules and restrictions") is more appropriate at the moment.
We see here a Harry who chafes under the restrictions imposed by the Secrecy Statute and is eager to test its boundaries, even if that behavior gets him in trouble with the Ministry of Magic, the Muggle world, or both. One can almost see him charging into Radcliffe Hospital with wands blazing, if needs be, and ending up in a Muggle jail. (That would be an interesting development.) We hope he is more intelligent than impetuous, or, as Hermione would say, has a good plan. It will be fun to see where this story goes.
This is one of the most interesting fanfics I've read in a while. I really loved all of the parts of the series set in the Muggle world, and I think you've handled the Muggle-Wizard connection well. I really like adult-Harry, he reminds me a bit of Dumbledore, which makes a lot of sense. The Dursleys were also characterized very well.
I really liked this read, It was really well written, but why is the text all weird? I don't know if it's just my computer or what, but it made it difficult to read. Other that, good job because it was so interesting.