The bomber/parka jacket theory. They never quite specified what they thought had happened - Luke was wearing the bomber in the afternoon at school, and later, when he was taken to the police station after Jodi's body was found.
But here's the bit I find really interesting. On August 14th, following the second raid, they were grilling Luke about what he was wearing the evening of the murder. They claimed to have more than 50 witnesses, all describing Luke "to a T" wearing ... ready ... a German army shirt. Not a parka, not a bomber jacket, but a German Army shirt. The very next day, the first pictures of Luke wearning the parka his mother bought after the murder (the police had the receipt) appeared in the papers on August 15th - the very next day.
Luke was never questioned about a Parka, missing or otherwise, until April 2004, 8 months later, yet police claimed their "suspicions were raised" when they searched his house and found the parka "missing." That had to have been the raid on July 4th (since by August 14th, he had a parka, so there was no "missing" parka.) But by July 4th, there were no statements about Luke and a parka, nor even by August 14th (as evidenced by their line of questioning.) As a matter of fact, the first statements about Luke wearing a parka began to appear ... after he was pictured in the media wearing one.
So, what about all these witnesses saying they'd seen Luke in a german army shirt on the evening of the murder, directly after the time it was claimed Jodi was murdered? Why weren't they all paraded into court to challenge the "parka witnesses?" After all, the claim has been that "all those witnesses" (to the parka" can't have been mistaken, yet it appears we have 50+ witnesses who were all mistaken about the army shirt?