Just to give an answer or opinion to one or two of these.
*Was Jo vegetarian, did she like that type of pizza enough to have it when by herself, or even enough to finish the left-overs the next day? Or could she considerately have bought that type of pizza to please someone else?
I read somewhere something about there being a reference to glazed ham that suggested she wasn't vegetarian. But take that with a pinch of salt [boom boom].
*Was the cat starving, traumatized, soiling everywhere? If starving, wouldn't he have miaowed loudly - did the neighbours hear anything? Where was the cat? Does he use a litter tray or does it go out - if so, is there a catflap, does he go through a window, does he miaow to have the door opened? Was LL ok about them having a cat (some of them don't allow pets)?
No cat flap. We understand that cat was inside. CJ must tolerate pets, since there's no way he couldn't know about the cat over time. My assumption has been litter tray, without there being a cat flap.
Greg said that the cat was "going mad" when he arrived home. [NB: as is often pointed out, this should have been a major alarm bell, surely. It will either have been starving or will have soiled in places.]
*What state was Jo's other sock in? If she'd gone out in her socked feet (which I find hard to believe - after dark, it could have been wet, muddy, you name it, not to mention freezing cold), the other sock would probably show it. Did Jo have slippers? Are any footwear, hers or BF's, missing from the flat?
You have almost certainly seen the sock, so make your decision!
The sock in the news conference is likely to have been the one found on Jo. The police were forced into releasing the info after The Sun leaked the story of a single sock. [Can we say that they were caught on the hop? [Sorry]]. They didn't have time to find a similar sock to show, so that's why the one we see is in an evidence box, I believe. We see that the heel is a little worn.
We aren't led to believe that she had slippers or anything, nor that shoes are missing from the flat. But then, as with all this, we're not told much.
*If Jo's parents knew within 30 minutes of entering the flat that she didn't go of her own free will, how come the BF, who lived with her, waited for hours before panicking?
This is quite frequently discussed. And [even though I think it remarkable that GR doesn't see anything that leads him to call the police] you have to appreciate that it's a matter of perspective that can make the difference.
Condition a) that you come home and your girlfriend isn't there is a very different from condition b) that your daughter has been reported missing, it's now a police case, and you go into a room to see what you think.
In other words, the difference could be [although may not be] that Jo's parents were *looking* for something, which Greg was not.
Actually, 30 minutes is quite a long time. So we're not talking about splashes of blood across walls etc.
In those 30 minutes they may, say, have looked around the bedroom examining things and found, say, that Jo hadn't taken her pill for a few days [if it was something she took, of course]. Or they might have charged up her phone [if it was out of battery] and seen that she hadn't made any calls all weekend. Such things would be obvious signs of trouble but not signs that Greg missed, because he didn't look for them.
[I actually think it amazing that he *didn't* look for them, but there we go].
*Re. Glenis Carruthers murder in 1974: is there anyone who would fit the description of her killer that whose age and description fit loosely to someone who is still around today? "Fit loosely' because it's very easy to misjudge the height or age of people. Especially in the dark, from a distance, etc.
The A&S Police site says: "The witness described the man as white, between 20 to 25 years old; around 5ft 10inches tall in height, medium build, with brown shoulder length hair. He was wearing a three-quarter length coat and a denim type cap."
I think I posted something to do with this yesterday.
*Would a perp unknown to Jo really move the body?
In my opinion, absolutely not, if the murder took part inside the flat itself.
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Your questions are very interesting, but sadly a lot can't be answered by us armchair detectives, because we just haven't been given that many facts by the police.