When Dorian serves Ethan Absinthe, after adding ice water to the liquor, it should have turned cloudy and milky looking with a lighter green color to it. This is a phenomenon called the "Louche" Effect and is a defining trait of the liquor known as the Green Fairy. In the scene however, the drink stays the same bright, translucent green it was before the addition of the ice water.
Sir Malcolm mentions that discovering the source of the Nile is a 'holy grail' for explorers. However, the series is set after Jack the Ripper was active (the late 1880s) and the source of the Nile was located by John Hanning Speke in August 1858. An educated man like Sir Malcolm would surely have known this.
The inscription in Ethan's watch ("To Ethan from your Father") is in an outline version of a font published in 1949: Palatino, designed by Hermann Zapf (1918-2015).
At the botanical gardens, Dorian Gray incorrectly characterizes the flower Miss Ives is admiring as "Atropa belladonna - deadly nightshade". While the plant shown indeed appears to be of the nightshade family, the shape of the flowers indicate a specimen of the Dulcamaroid clade (e.g. bitter nightshade (Solanum endoadenium) or bittersweet (S. dulcamara)), rather than belladonna, which has a bell-shaped flower in a more muted mauve/purple color.