When the Durrells arrive in Cofu, Gerald is seen looking at a lizard in a tree. The lizard shown is an Inland Bearded Dragon, a species native to Australia, and not found in Greece.
Leslie refers to Margo's bikini; the bikini was invented (and so named) in 1946, 11 years after this show's setting.
Margo is shown only slightly sunburned after multiple days sunbathing in direct Corfu summer sunlight without sunscreen. She is a freckled redhead, and therefore would burn gravely under such conditions, likely to the point of hospitalisation.
Margo's two-piece swimming costume is referred to as a bikini - a term not used until 1946 although the episode is set in 1935.
Margo says "it's going to be different than I thought". "Different than" (rather than "different from/to") is an Americanism which did not enter common British usage until the 21st century.
In the first scene in the Durrells' Bournemouth kitchen, there is an Art Deco style clock, which while correct stylistically, carries a brand name of a modern company, Newgate.