A title card states it's Thursday 14:01 but two scenes later when Quentin is asking Mary what she's doing that evening, she says "I usually help Mum with her bath on Wednesdays."
Christine is picking up her glasses from the table, then in the next shot as Joseph hands her paper she's already wearing them.
As Jerry's talking to Christine, the shot of Jerry shows Christine's holding her glasses in the air - but in the reverse shot on her, she's not.
In preparation for his cartwheel, Tom takes off his bag, dropping it on the floor with his jumper, but when Jerry suggests going for food Tom walks off without picking anything up.
During their meeting, the page Tuva's looking at on her tablet changes between shots.
When Barnaby's seminar is hacked, the GCHQ twitter shows a previous tweet saying their director is "Christine Clarke" but in Episode 1 she is introduced by Joseph as Christine Cranfield, and in Episode 6 her email is shown to be christinecranfield@cybersec.org.uk.