The way I understand it, MOR is meant to be an example of how a rational being might go about approaching a completely new and confusing set of observations, such as discovering that magic is real. However, I think harry has missed a lot of the low hanging fruit he could be researching. Although my suspension of disbelief shut down these thoughts pretty fast when I first started reading, I was always pretty curious about why magic was created in the first place, why only certain people could control it, and how exactly the energy needed for spells was obtained and applied. So here are a few things I would want to research ASAP if I was harry.

A) Is it possible to fool the source of magic (sm) so that it allows a muggle to cast spells? It was pretty safe for harry to rule out the idea that your DNA contains all the information needed to create a complex mechanism which can generate a magical field and respond intelligently to your intentions, so it makes sense that your DNA only serves as a signal that tells an external force to activate spells when you verbally or non verbally cast them. However, this raises a few interesting questions. does sm actually read everyone's DNA constantly/ whenever they try to cast a spell? or does the sequence of DNA cause a more obvious external change to your appearance that sm looks for? If it uses something like the pattern of your brainwaves, the shape of your face, etc as a marker, then it may be possible for a muggle to mimic a magic user easily and vice versa, but if it actually DOES read your DNA, then where? Could you grow a heart using a magicians DNA, have it implanted, and acquire magical abilities? For that matter, if you preserved the body of a dead wizard, and set up a electric transmitter in their mind which mimicked the signals sent when someone cast a spell, what would the effect be? Any recognition system should be possible to fool, and this would be the most important thing to test for me. Imagine being able to give every person dying of thirst or hunger in the world unlimited access to the resources they need. there would be no more third world countries, although you would also be distributing a terrible weapon.Which actually brings up another question...

B) Why on earth would you invent a powerful system for allowing someone to directly effect reality with their thoughts, and then let everyone with the right DNA use it with no inhibitions whatsoever? Avada Kedavera, Imperio, and fiendfyre may have their uses, but I would not let all of my ancestors use them without supervision with no more training then it takes to cast any other kind of spell. It would be as idiotic as giving everyone I knew the codes required to launch a nuclear missile whenever or wherever they wanted too using their cellphones. Even if they all had good intentions, someone is going to make a dumb mistake eventually. Creating a system for inhibiting the use of such spells would be complex, but only an idiot would not try. This has several implications for harry, either magic was invented by a moron, there are even MORE powerful spells out there that he could cast if he knew the access codes (!!!), or someone already found out how to game the restrictions so they fell apart long ago and nobody even realizes they exist, you may even be able to get it working again.

C) the SM has to have a a sustainable energy source somewhere, a method for using this energy to create the effects we call spells, and in order for it to perform the complicated routines needed to assess someones intentions, it probably has to be somewhat intelligent. Somewhere out there may be an AI, a group of slaves being used to perform observations and calculations, or the work is being sent on a distributed computing network to the minds of every sentient being on the planet. this may be the hardest thing to research since there are almost an infinite variety of of possible systems which may be the cause, and it is probably concealed. But, If you could find the physical source of magic, you could reprogram it to do whatever you wanted, and could achieve world peace or destruction in one step

I would write more but I am honestly hoping for people to actually read through this and give their thoughts, so I guess I had better stop now in the hope of remaining somewhat concise.