When DI Goodman finds the bottle with the poison in the hotel room, there is only a bottom left in it. When he picks it up from his desk at the police station later on, it is at least half full.
DI Humphrey Goodman is checking the room where the crime was committed. In the close up of him looking through the items of the person, he not wearing gloves. Immediately after when the camera shows the whole room, he is wearing a glove.
When it is discovered that the room key is missing for Natasha's room, the front desk person goes to the room to check on her. However, on the door is a sensor pad, commonly found on doors that require a key card, not a key.