But if as you say the killer had bloodspatter on him from his victims, if he got out of a window wouldn't there have been a very real chance that he would have transfered some of that bloodspatter onto the window or the sill?
Only if the blood was on his hands and wet. Blood doesn't transfer from clothing to objects unless there is a considerable amount of wet blood. Spater is droplets that soakes into the clothing and it dries fairly quickly.
I don't believe Jeremy would go home with blood on his body. He washed any blood off his body. How would it look if someone happened to be outside as he was walking into his house and saw blood on his body? It also would have been wise to bring a change of clothing and dispose of the clothing on the way home but whether he did we have no way to know. Even if he didn't though his clothing would not be likely to drip blood onto anything.
Most if not all spatter would have been from the first 2 victims. Jeremy didn't just bolt out the door after killing everyone, he staged the bullets, bible and other things. Both of these gave time for the blood to dry before he left.
I personally think Jeremy was stupid and kept a spatter stained jacket and just tried to wash it but at the same time was very lucky that it was tested so late that the blood had already deteriorated too much. Police found a jacket that has red marks that looked like spatter when they searched his house. He calime dit wa spaint. When you paint you get a couple of drops not a ton of hem closeby unless you flick your fingers through the bristles of a brush in a direction way from your body so that as the bristles snap ack they fling a lot of drops in close proximity. Why would anyone do that though? It is much more likely given the circumstances that it was spatter than that he did the aforementioned with a paint brush. He washed it and that combined with the time was enough to prevent them from getting any test results. With today's technology he would not have been as lucky.
If police had been wiser and searched his house close to the time of the murders he would have been busted over this if it was indeed spatter.
I honestly wonder why so many criminals keep spatter stained clothing with the intention of washing it. It makes no sense to me and yet it is a common occurrence.