Whilst it's possible in England and Wales to exclude a current spouse from the will, (testamentary freedom), there is another law (Provision for Family and Dependents) Act 1975. The Act sets out categories of people that have the legal standing to challenge another person's Will on the basis that they have not been left reasonable financial provision.
The victim would not have been "eaten by wild boar" as it is the females that are sexually attracted to truffles, so it would have been wild sows that would have attacked him.
Only the white truffle would be sufficiently valuable to be a motive. These are usually harvested from November to March, whereas the filming took place in summertime.
Paint fumes can be fatal to dogs and cats.
Nelson's brute force attempt to break into the laptop could have irreparably altered the computer evidence so that it would be inadmissible in court--assuming he could even get to the evidence. Nelson should have let the computer forensics team look over the computer, to ensure the integrity of the evidence.
Not even Gordon Ramsey would complain something was cooked for 15 seconds too long.