During The Adventure of the Cheap Flat, the flashback involving Poirot telling Hastings about the original theft of the plans has a very bizarre feeling to it compared to other times Poirot tells about how the crimes he later investigates were committed. In fact, it doesn't look like the real world at all, but rather a highly stylized gangster flick, down to the way the characters speak to one another. That's because it isn't what actually happened—this is Hastings' Imagine Spot, and given he's recently been watching a gangster flick...
During The Adventure of the Western Star, Marie Marvelle and Poirot speak in English to one another throughout the episode when together, which seems bizarre given neither of them are native English speakers...until there's a scene when the two are alone and speak French, which remains untranslated for the audience. They were likely speaking English in previous scenes out of respect for others present who might not have spoken French.
Small one that applies particularly to the adaption of The Mysterious Affair at Styles, but can probably apply to the original as well. Hastings is referred to as "Lieutenant Hastings" throughout the episode, but gets a promotion to Captain at some point before the rest of the series. Does this mean that Hastings, who'd already received some sort of injury prior to Styles and was strongly implied in the series to be suffering from shell shock, went back to the front?