Same goes for the bathroom window
I think there are more conceivable scenarios for a bathroom window to be open than the balcony of the room where your small child is sleeping open.
Off the top of my head it could be for a hot bath to avoid fogging or just for general ventilation sake to avoid a swampy feeling
Its also far more easier to ascertain whether the bathroom window is open or not, as Incoherent has mentioned.
If we accept the premise he had been watching them, I don't see that as a challenge per se. Moreover, we know that he paced beneath the bathroom window. Why couldn't he simply have tried. He tries the bathroom window first, then goes to Rei's. Either/both is possible
The problem with this is there would be mud on the balcony, in the house all throughout. Unless he cleans it off. He only has his hankies so its either than, some other clothing on him or some stuff on the grounds to wipe off the mud.
Even that might not be 100% efficient from a forensic perspective.
Its possible that this is indeed the case, but it has not been disclosed by the PD, but as we have no info, its a valid argument against it, unless proved otherwise.
As with the front door, we don't know if it was open or closed when LE arrives. But at any rate, what stops him from closing the balcony window/door?
So its not a problem in and of itself. The problem arises with what he does with the bathroom next. If supposedly he came via the balcony, he has no reason to shut the door, unless he wants to obfuscate his mode of entry.
But then he does the thing with the window screen, implying that to be either the mode of entry or the exit, which kinda seems excessive and a bit redundant, since he has already taken care of his mode of entry.
That would make sense only if he chose to exit via the bathroom window, which might explain the muddy print below the wind but would imply that while the killer is ok obfuscating his mode of entry, he is ok to leave behind clearly his mode of exit.
Now this is possible if he was pressed for time, although we don’t have any evidence for or against it.
My point is that is that there is no complaint of a break-in prior to the murders. Either here, or in the area. Is it possible he was entering the Miyazawa house without leaving any trace? Yes, sure. What are we basing that on--that it's hard to fathom that he would try to climb through a window without previous break-in experience? I don't know, at some point it would have to be the first time.
There are no direct complaints yes. But we do have certain indicators that something was indeed bothering the Miyazawas. They also for some reason believed that this was related to the skaters.
It might not be something as egregious as breaking in, but something less sinister like peeping, peering or something, which would unnerve a family but might not result in a police complaint.
Anyways, the gist of it is this. The killer might be more experienced in breaking in and entering, not just particularly for the Miyazawa house, although he is still a very inexperienced killer and has never been caught or convicted of anything before or after this.
We don't actually know that, technically-speaking
Yup, but I think we can infer that.
This inexperienced killer doesn’t account for blood, he infact is not even very confident of taking on an injured woman and child without a knife.
Does this psychologically speak of someone who is full of confidence with regards to his kill? Or is it someone sharp, who is using every advantage that he has in his book to maximise his success rate?
I think its the latter, and so if you extrapolate that thought process. Why would he randomly attack a house that from the outside, looks like it might be two houses joined together? Rather than a single isolated house.
How does he know not to go in the garage to look for stuff ( if he was even looking for anything)? How does he know there is no one in there, or a tunnel that connects to the other house?
This might seem a bit silly in hindsight, but I don’t think the killer would have gone into the houe without having used every advantage in his book, which would include some basic info about the house layout.
But, if we accept the premise that the bathroom window is the most logical entry point, then what would be so puzzling for the TMPD?
I am guessing the TMPD are stickler for details, and because they have no physical evidence, they are hesitant to commit to anything.
Just my take on it, you obviously have more feel for it.
As for the lack of physical evidence, you are right, and I have no knowledge about what is possible or not possible in this regard. So yes, thats definitely a problem in this theory.