Let's start with the points on which we are on the same page...
Assuming it's true, I am bothered by him burning clothes shortly after the killings. What exactly was he burning?
Was it just clothes or was that a pretext for destroying other things more incriminating, like clothes of his own he was trying to hide? I am given to understand that the police were not searching him at this point.
Another one that bothers me and may not yet have been mentioned is his decision to have his parents and Sheila cremated. Why would he do that? I expect cost of burials may be advanced as a reason, but would it really have been much of an imposition?
Cremation is burning, and burning implies destruction and disposal, and bodies are key evidence, and Jeremy would be at least vaguely cognisant of this and would realise that if the investigation ever turned course, the police would want to exhume the corpses.
So there's another one for you, if it's not on your list already. "Just because Jeremy insisted on cremation, doesn't mean he is a murderer." It doesn't, but it IS suspicious.
Now, turning to where we disagree...
The word 'normal', to me, has a firmer meaning than the word 'inappropriate', which seems more in the eye of the beholder.
But let's move away from semantics.
If I was a detective and saw a family member grinning at a funeral, I wouldn't be suspicious about that in and of itself, but depending on the context, it could be viewed as inappropriate, so I would make a note of it.
Now, this may mark the beginnings of a veritable dossier of such behaviour, recurrent across varied situations, in which Jeremy is seen laughing and joking in the face of mourners, telling smutty jokes at funerals, selling antiques, ruthlessly having dogs put down, enjoying hearty breakfasts and indulging in sex and travel in the sun, but that would not necessarily amount to a 'pattern'. A pattern suggests structured or planned behaviour (behind which may or may not be criminality).
I would want to avoid templating patterns in retrospect on to innocent behaviour. It would be an understandable mistake to fall into, especially since Jeremy Bamber probably is a mass murderer. But the 'pattern' you infer from various facts is not what makes him a mass murderer, and I think my whole objection arises because most of the points raised seem quite airy-fairy and subjective. It's stuff that a detective should note, but it's not evidence.