When Kitty and Jack are sitting at the table discussing his voluntary post on the China station, Jack takes Kitty's hand; when the scene cuts from the mid shot to the long shot, their hands are nowhere near each others.
Mother Riley throws piles of wet laundry fresh from a sink at the supervisor, totally soaking the woman's hair completely. Supervisor shows up two minutes later with hair that looks dry and only slightly out of place.
In the Pub scene when Mother Riley goes in with a jug to buy beer, Jack puts a cigarette in his mouth and tries to light it several times to no avail and while Mother Riley and the bartender prattle on, Jack as the unlit cigarette in his mouth - however, when it immediately cuts to the back shot, Jack is standing with the cigarette in his right hand.
When the gas runs out and Mother Riley puts a shilling in the meter, the gas is left running for some time on full blast - the moment Jack lit that lighter near the stove, it would have exploded much sooner than when Mother Riley tries to light it.