Oh! To Be in England (Part 1 of 2) - S2-E1
Continuity mistake: When Mademoiselle Dupont is arriving in the car, Ma and Mariette are standing in the garden, holding their babies, John and Oscar, and waving at the car. Then Mademoiselle Dupont steps out of the car and they run to meet her. Mariette is still carrying John but Ma is no longer holding Oscar. He isn't sitting on the ground and no-one else is carrying him either.
Stranger at the Gates (Part 1 of 2) - S2-E3
Other mistake: In a previous episode ("A Breath of French Air") Ma explains to a french fisherman that she's used to cooking fish as the Larkins have both a pond and a river near their home. In this episode Montgomery complains that there is nowhere around for him to fish.