Goofs

Boris Yeltsin was missing a thumb and an index finger on his left hand. According to him, he lost them in an explosion as a child when he tried to disassemble a grenade he found. In the episode, he is portrayed with all of his left hand digits intact.

George V and Queen Mary are shown to have English accents. In real life both spoke English with a slight German accents.

When Prince Philip is explaining how scientists took his blood for a DNA sample, he shows Lady Knatchbull a photo and explains that the pattern of bands is his DNA. The lanes are labeled ATCG implying each lane contains one of the four bases of DNA, but that's not how DNA analysis works. You don't separate out the bases of DNA in a gel.

The gel does not separate bases, it is the result of Sanger chain-termination sequencing used extensively in the 1990s. Each lane runs a different extension reaction on the same template containing one of the four dideoxynucleotides and separates labeled DNA fragments of different sizes that end in the corresponding nucleotide. In any case, for forensic identification, it is more likely RFLP would have been used.

At around 23:00, when the human skull is placed of the table, it is obvious from the barely hidden horizontal division line that the skull is from a plastic skeleton as used for educational purposes.

The opening indicates the action takes place in 1917. Consideration by the British to send a ship to evacuate the Romanovs from Russia occurred in the spring of 1917, when the provisional Russian government was still in power. The scene shifts to Ipatiev House in Ekaterinburg, Siberia, where the Tsar and Tsarina speak of their cousin, King George, sending a ship to rescue the Imperial family. The Romanovs were imprisoned and later executed in the Ipatiev House by the Bolsheviks (who were then in power) in the summer of 1918, more than a year later, by which time the Tsar and Tsarina were well aware that the British were not sending a ship to rescue them. Moreover, Ekaterinburg is thousands of miles away from any seaport.

Both characters of Tsar Nicholas and Tsarina Alexandra are shown to make the Sign of the Cross on their bodies. This is made with an open palm (in the Roman Catholic manner), as opposed to having the thumb, index and middle fingers joined together (in the Eastern Orthodox manner).

The Tsar and Tsarina are shown to be speaking to each other in bed at Ipatiev House in Russian, but it's been documented that they usually spoke to each other in French or English while in private, as the Tsarina's Russian was very poor.