Neighbour's keys might well have been retained. That still doesn't make me happy about how JeM was getting access to the house on the day Bob went missing though. How he was able to 'let' the CL in the back door when he returned from one of his shopping trips?
I have two reasons to think that back door was locked. When the CL lady found no answer, no key in the mail box and was worried, wouldn't she have tried round the back too? If it was open, why did she need JeM to let her in? If there was a locked gate stopping her - again, how did JeM get in?
Second *reason is it now looks like JeM left the house before the CL and returned after his home depot visit, when she had already left. So did the CL lady just go and leave the house unlocked? Even though she was so anxious something ominous was in the air?. I think she locked up after herself. *
So again, how was JeM getting in and out of the house that day? And if was carrying around a spare set of keys for Bob's from home I have to ask why? If he didn't expect Bob to disappear and then thought Bob had just gone for a walk........at some stage that day he should have found himself locked out.
So, to sum up;
No keys means JeM was running in and out all day leaving the doors open and left the house unlocked for the night when he finally left. But at the same time, the CL couldn't get in herself. Doesn't make sense.
With keys means JeM either brought some from home or took some from Bob's house on his shopping trips. Doesn't make sense, if he was expecting the owner of that house to be there to let him in.
And don't forget the strange little 'JuM knows where the safe keys are' remark in that list. Kind of hints that JuM knows where they are, isn't telling anyone else and is fairly confident they will still be in that hiding place in Bob's house when she needs them. I hope LE was informed about this secret place the night they did the welfare check. Just so they could check and make sure Bob's missing keys were not in the house after all. That could have been very, very significant and put a full search for him in motion straight away.
Like the timeline, I think there is another story behind the missing keys, just waiting to be told.