When Tim Kono enters the elevator, he presses the button for Floor 8 but the elevator's digital display shows him getting off at Floor 9.
At the beginning sequence, Charles, Oliver, then Mabel get on the elevator in that order.
Charles selects Floor 14. Mabel selects 12, and Oliver selects 10, in that order.
But shortly after the podcast sequence, they show the window exteriors of the 3, starting top to bottom, and Charles, Mabel, and Oliver are shown on adjacent floors. But unless they skip a 13th Floor, they would still have an 11th Floor between 10 & 12, Mabel and Oliver wouldn't be on adjacent floors.
Before the memorial service, Oliver (Martin Short) takes a bite of a carrot, then as he crunches on it, the camera pans away. The next scene he is holding a stick of celery.
Oliver starts to record audio with his phone. As he's holding it up, you can see that the phone is actually not recording, but is playing an audio file. In fact, the file is paused and shows that it has been played a bit, although none of the file was heard.
At the beginning of the episode (07:51 to be precise), Mabel is supposed to be listening to a podcast at the same time as the others, but if you look at the phone on her bed, the screen shows a play symbol which implies that whatever she is listening to is paused.
In the opening sequence introducing Oliver, the car that almost hit him on the pedestrian walkway was obviously static and pushed up and down by off-screen crew behind the boot.
At around 09:30, when the fire alarm goes off, the podcasts on all the computer stop playing audio, even though none of the computers or phones were paused.
At around 02:15, Charles takes a picture of a couple. His finger is partially over the camera, so the picture would have been blocked by his fingers.
At around 28:30, Charles looks at the Amazon prime box belonging to Tim Kono, before questioning where the box is.
No police force would leave the crime scene completely unguarded even for the brief moment the three crime-solving musketeers spend checking on dead Tim.