Okay - a few thoughts. There are definitely still threads left hanging. In no particular order:
* LR's phone: found in a very bizarre location. It was lodged half under various detritus in the alleyway. Any explanations? How soon was it found?
* Who reported LR missing? How soon?
* Absence of evidence that Halliwell was involved is not evidence of his NOT being involved, IMO.
* GR - there is a ring of authenticity about some of his assertions, IMO (changed his clothes, forgot to give both sets of clothes, he paced around on the grass to clean his shoes etc). The blood is very worrying. It's also frustrating that the hooverings from the car can't be tested.
* The car: where is it now? Is it not still in evidence?
* polygraph: not sure what to think about this. I kind of agree with GR about how they can't be reliable. We have a scepticism about their use in the UK I think, much more than in other legal systems.