In the scene where there are prayers in the house of mourning ("Shiva") the men and women are seen as intermingling. However, in a very orthodox Shiva service there would be complete separation of the genders - indeed, in a small house, such as the one depicted, they would be in separate rooms.
Whilst waiting for the tube (subway) to take them to the West End (centre) they appear to be on a platform of an underground station. However, the station they would have gone to would have been Golders Green, which is outside (not underground). Whilst on the train they are shot in close-up only but you can see into the next carriage which is completely empty (very unlikely in a train from Golders Green).
When Dovid Kuperman is sitting at the start of the service for the rabbi [1:34:23] there is a stack of religious books. Two of these are upside down in relation to the others which is forbidden in Jewish Law.