Sarah and DCI Barnaby's baby in the hospital, following the birth, is different to the one shown on her return to their home.
Calder handles the tin of biscuits and begins to feel the effects of the Strychnine in a few seconds, but Strychnine takes 15 to 60 minutes to affect it's victims, not 15 seconds.
The Coroner says a PhD is needed to synthesize Strychnine. Anyone with a degree in Chemistry could do it if they had the chemicals and equipment. There is more than one way to do it, but the oldest, the Woodward Process requires more than twenty (20) steps, special chemicals and specialized equipment. Strychnine has seven rings which must be synthesized one by one, so it is not a simple matter of pouring chemicals into a flask and voila it is done. The lab in the biscuit factory would not have the equipment nor the raw materials.
Barnaby and Nelson's taxi passes Amalienborg Palace (residence of the queen, the crown prince and other members of the royal family), but that would be a detour when driving from Copenhagen Airport to the police headquarter, and you will not pass that many flat motorways on that tour, unless the taxi driver cheats foreign customers. From spring 2020 it is not allowed to drive cars in the Palace square.
Barnaby comes home snatches the biscuit tin from Sarah and tells her no more Calder biscuits in the house for a while. His explanation is that it was a tin of biscuits that killed Calder. While a cute conversation, it is illogical since Calder was killed with poison on the OUTSIDE of the tin and Sarah had been handling the tin and eating the biscuits when he came home. If the tin or biscuits were poisoned, she would already be dead judging by how quickly Calder died.
Both Inspectors Barnaby tended to delegate chases and other forms of exertion to their younger partners. But John's simply standing on the factory steps while Charlie struggled with a rescue was too non-heroic for the character, or any protagonist.