PK slashes himself with chain blades during a Moharram festival religious practice. Later when he removes his shirt in front of Tapasvi he is shown with no marks on his back. When someone slashes themselves with chain blades the skin breaks and bleeds. Later there must be marks of the new skin.
In her entry scene, Jaggu is shown locking her bike and then she heads towards the concert. After she ruins old guy's suit, Sarfaraz is shown to immediately ride her on the same bike while she was being chased by security guards.
In one of the scenes, an elderly person asks PK for Rs 500 as he was Rs 500 short for the treatment of his wife. PK gives him Rs 500 plus Rs 100 for tip. In previous scene in temple, when Jagat Janani's money was taken away by temple's priest, Pk offered her Rs 200 which he had taken out from temple's charity box and also said that he had no more money, while pulling out to show his empty pockets. So if PK had only Rs 200 at that time then he could not have lent Rs 600 (500+100) later.
When Anushka follows PK to the police station, her scooter parking spot changes in the next scene.
Jaggu listens to the tape recorded by PK, but PK was never shown pressing the record button in earlier parts of the movie.
In the final climax, which is on a Sunday at 9pm IST, Jaggu calls the University administration office at Belgium. Based on the Time Zone differences, it should be Sunday evening approx 5.30 pm CET. Her call is answered by an official, which is not possible, since its Sunday and its 5.30 pm.
Jaggu then calls the Pakistani Embassy, which should not have been answered since the Brussels Pakistani Embassy is closed on Sundays.
Towards the end Jaggu mentioned while narrating her story that PK came from a Planet 400 crore miles (4 billion miles) away from earth. This implies that PK's planet is very close to Pluto (4.67 billion miles). No such planet exists. Secondly, PK adapted to earth's atmosphere without any problems which implies that his planet must have a similar atmosphere. For this to happen his planet must lie in a Goldilocks zone. But we all know that 4 billion miles from earth is no where close to that.
PK throughout the movie says there is no need from language on his planet as they read each other minds, then at the tail end when he come back to planet earth with a research group, he is heard giving instructions to them in Bohjpuri, they should be able to read each other minds.
When PK is being pushed out of the church, the person says, "Jesus sooli pe latak gaya" [Jesus got hanged]. In response to this, PK's lips move as if to say, "Kya?" [what?] but instead the sound is "sooli pe!"
Pakistan Embassy in Belgium is located in Brussels not in Brugge.
The TV show at the climax of the movie is scheduled to being at 6PM in New Delhi. The evening light should be low/dim, while Jaggu's mother sits at her house with bright sunlight in background. If it is said that the show was not live, and instead was recorded, then Jaggu's mother could not have been watching it at the same time of telecast.
The scene of Jaggu traveling in Delhi metro shown after she received the letter from the boy in the church is actually from Mumbai Metro. The rolling stock and railway stations are of Mumbai metro.
The locomotive class (WCAM-3 KALYAN) of the train in which Sanjay Dutt arrived in Delhi to meet PK is actually only operative in Mumbai area. When the train arrives, the train indicator shows train no. 12290 which is actually a Duronto train running between Mumbai and Nagpur, which further shows that the scene was shot in between Mumbai and Nagpur.
The day PK landed in Rajasthan desert, he met a local near the tracks who was wearing a sweater, suggesting winter months. After his pendant was stolen, movie moves away to Europe stating "Later Same Day" where Jaggu was seen fighting for Amitabh Bachchan's concert ticket. The big blue colored poster with Amitabh Bachchan's face stated date as 5th June 2013. This implies that PK landed on 5th June 2013 in Rajasthan where the temperature should have been close to 40 deg C. There is no way anyone would be wearing a sweater. Also, after a while the movie jumps to 6 months ahead I.e. around first week January 2014, suggesting peak winters in Delhi. During this time all the characters are wearing clothes which would be worn in those low temperatures. This further confirms that PK landed during peak summers.
At the end when Jaggu listens her all the tapes PK recorded, while waiting for him there's a tape recording appears where we can hear Jaggu saying "tumhare planet pe sab ke kaan aise hote and blah blah" but at the time she says this in the movie PK had just woken up.
PK learns the whole vocabulary of the language from a "prostitute" but doesn't have any idea about the word "condom" which he comes across in the second part of the movie.
During one of the scenes where PK runs to save himself and boards the bus, the security guards running behind to caught him are laughing. Considering the scene, it was supposed to be hilarious for the audience and not for the characters.
When Anushka meets PK and he gives her money to go home, she asks him the reason for helping her, to which he replies that she is the first person who has ever given him money. But this is not true because during PK's narration the blind beggar in the street supplied him with money whenever he needed.