Character mistake: Poirot identifies Prof. Hardman's revolver as a 1927 police-issue weapon due to its blued finish and chequered grips. In fact, these features were common in the widely-available civilian versions of the Colt 'Police Positive' revolver and not the least bit specific to police-issue weapons.
Character mistake: In the scene in front of the Western Wall in Jerusalem Poirot says "In the Church of the Holy Sepulchre above us..." but the church isn't located there. It's northwest from there, in the Christian Quarter of the Old City. (00:04:10)
Answer: Not necessarily. Jerusalem is a meeting place of many religions and faiths - and there's nothing to suggest that the Catholic priest isn't there on holiday.
Except it's stated that priest was negotiating market use (with the imam and rabbi). He was a local.
Brian Katcher