The Kipper and the Corpse (a.k.a. Death) - S2-E4
Character mistake: When Sybil is telling Basil that the two men and the woman are coming to collect Mr Leeman but he's already pronounced dead, she tells her husband that they are coming to collect him "at lunchtime". However, his colleagues told Mr Leeman they'd collect him at 9:30 and not lunchtime.
On the Run - S3-E13
Character mistake: When Mrs Haldane is giving her statement to Regan she tells him that Cook was wearing dark glasses when she saw him outside her neighbour's house, but Cook wasn't wearing any glasses.