It's not clear how Bernard planned to meet Ben and Jo if Hank hadn't accidentally grabbed the woman's headscarf. The Arab man who yells at them is implied to be under Bernard's employ, so what was his original purpose? Presumably the Arab man would have found some way to threaten or inconvenience the couple, allowing Bernard to intercede and gain their trust. Hank's accident just so happened to provide a perfect excuse.
He wasn't looking for Ben and Jo. He was looking for a "suspicious couple." This is more of a case of Fridge Logic, because if Hank hadn't accidentally grabbed the woman's scarf, Bernard would have never met Ben and Jo in the first place.
And it's not established that the Arab man worked under his employ - rather Bernard was just asking him if he knew anything about Ben and Jo. On the other hand, there was a woman with Bernard which DID seem to be at least partly into his scheme, but we never got to know anything about her or her fate.
So the plot is to kill a Prime Minister. Does the film ever say WHAT COUNTRY he's Prime Minister of?
Nope. Never. I suspect that Hitchcock didn't want to offend any real-world nation. During the concert, there's a large flag underneath the Prime Minister's box, but it's a fictional flag that doesn't belong to any actual country. Though it would have been nice if they just came up with a fictional name for the place; the dialogue gets a bit awkward when everyone has to avoid mentioning the name.
Why were the Draytons in Morocco in the first place? They had an assassination coming up in a few days, so what were they doing thousands of miles from the chapel that acted as their headquarters?
As the dialogue shows, presumably they went there to hire an assassin they'd been hinted at for their mission.
I can see why Dr. McKenna didn't tell the French police about what he'd heard, having just been threatened and all that. But when they meet with the Scotland Yard guy, he already knows the whole story about the kidnapping, and also this is hundreds of miles from Morocco and it's very unlikely that the assassins are listening in. If they'd just told him what they knew, they could've gone to Ambrose Chapel with a alot of backup.
They made a mistake. Simple as that.
Bernard was a French intelligence officer, right? So why do the French police treat Dr. McKenna with suspicion? They talk about how Bernard delivered a message to McKenna, so clearly he trusted McKenna. McKenna says that, if that were true and he really was Bernard's friend, then he would keep Bernard's secrets safe for him. The French policeman suggests that he might want to violate that confidence. Wait, what? What's going on here? The whole conversation seems to be based around the idea that Bernard was a criminal, and they suspect that McKenna was his criminal pal and thus he refuses to divulge some sort of criminal secret. But Bernard was a member of French intelligence, and McKenna is talking to the French police. Those two groups are on the same side, aren't they? I get that McKenna has his reasons for keeping secret (he's just been threatened), but the French policeman should be expecting McKenna to cooperate, and he should feel baffled when McKenna refuses. Instead he approaches the whole thing like a low-intensity Perp Sweating routine. This air of suspicion just doesn't make sense.
Wait, were the police chasing Bernard earlier? Or were they just chasing the guy who eventually stabbed Bernard? If the former, maybe they thought that he had turned traitor for some reason? Actually that whole thing is confusing. Police were running around. Bernard was running around. Some guy stabbed Bernard in the back, and the police saw this and they ran after the killer but nobody stopped to help and/or arrest Bernard. Not sure what was going on there.
The bad guys knock out Ben and then leave him locked up in Ambrose Chapel. Uh...why don't they just kill him?
Even Evil Has Standards, apparently. They're reluctant to kill Hank later on, so I guess they want to keep the body count as low as possible.
Jo conspicuously exits Ambrose Chapel. Why do none of the conspirators try to stop her? Even if you don't want to make a scene, you could still just quietly walk out the door and try to intercept her before she can get to a phone booth.
Jo calls Scotland Yard after leaving Ambrose Chapel. The guy who picks up explains that his boss is unavailable because he's attending a concert at Albert Hall. Later on, Jo goes to Albert Hall herself in hopes of talking to the guy. Is it just a bizarre coincidence that Albert Hall is the location of the planned assassination? That seems really unlikely.
Why does Ben show up at Albert Hall? As far as I recall, no one ever mentioned it to him. The only clue he ever had was "Ambrose Chapel". None of the conspirators mention where they're going. Jo was on her way to Albert Hall, but she never contacted Ben to tell him that she was going there or that Albert Hall was a place of interest. As far as I can tell, Ben only shows up because the plot says so.
Maybe, like his wife, he called Scotland Yard and was directed there.
After the failed assassination, the McKennas get word that two of the conspirators are at "the embassy". Presumably they have Hank with them, and they might well decide to kill him at any moment because he has Outlived His Usefulness. So Jo calls the Prime Minister and gets him to invite the McKennas over as thanks for saving his life earlier. Wait. They're on the phone with the Prime Minster here. Why don't they just tell him everything? "Sir, remember how somebody tried to kill you earlier today? Well, two of his co-conspirators are with you in the building right now, and they probably have our son with them. Can you get your men to run a sweep of the building? We'll tell you what the conspirators look like. Oh, and please give Scotland Yard permission to send in a bunch of their own men too." Sounds like a winning plan!
The one thing I can think of is that they were worried that someone else might be listening to that phone call.
The heroes may want to avoid an hostage situation, and to leave the possibility of a "clean" resolution to the kidnappers. The kid is still useful to them: if he was to be killed, nothing would prevent the McKennas from pointing out the conspirators.
Jo sings for the Prime Minister's guests. The plan is to keep them all distracted while Ben looks for Hank. But for some reason, Ben hangs around for what feels like fifteen freaking verses of "Que Sera, Sera", all the while knowing that his son is in imminent danger. He makes a super slow exit, as though he really doesn't want to seem rude. Just leave the room, man! Tell them you need to use the bathroom or something. It's all the more ridiculous when Hank starts loudly whistling to signal where he is, and Ben still doesn't leave, and by the time he actually leaves Hank has stopped whistling so now it's presumably a lot harder to find him (though somehow he finds him anyway). What's going on here?