When Jupiter is having the seal tattooed on her arm, it is just below the cuff of her jacket (near her elbow). When she removes her arm, it has moved a couple of inches down her arm towards her wrist.
In the scene after Stinger heals Caine's wound, as the camera switches between the two, Caine's wound reappears for a few seconds.
Jupiter applies the sanitary pad to Caine's wound over his jacket. Later on, he removes his jacket to reveal the pad which is now underneath his jacket.
Jupiter's iPhone 5 sometimes has the IOS 7/8 UI and sometimes has the IOS 6.
When Kalique Abrasax is talking to Jupiter in the room with her mother statue, for a split second while Kalique is talking, a yellow stain is on her face beside the left side of her lip and gone in the next scene.
When Jupiter and Balem are falling, they fall dozens maybe hundreds of feet then catch themselves. such a fall would have ripped their arms of their sockets and in her case ripped the skin off her hands.
The first time Jupiter is shown scrubbing the bowl of the toilet the seat is down. This is not something that anyone who knows how to clean a toilet (including actresses) would do because the brush would drip onto the seat. Apparently they caught this error and had her scrub it with the seat up the second time.
When Jupiter's father is peering up through telescope in their apartment, it is obvious that the telescope is empty of optics.
Jupiter's father in St. Petersburg has a brass-bound telescope, an expensive antique with poor optics that would not be used by a serious amateur astronomer. These scenes must take place in the 1990s,, when St. Petersburg was still recovering from the Siege of Leningrad, the longest, most destructive, and most lethal siege in modern history. There were decades of severe economic depression with food rationing, infrastructure failures, and multiple families lived together in 'kommunalkas' ('communal apartments') that would at most house a single family in much of the rest of the world. Luxury items like modern telescopes would have been completely unobtainable. Even antique telescopes with poor optics would have been seen as decadent and would likely have been traded outright to benefit one's family or, as in the film, stolen by others.
The alarm clock sounds even though there is no light that indicates that it has been set. Some clocks may do this but most do not.
When Jupiter notices Caine's wound, she takes a sanitary pad from the glove compartment of the car. She puts the non-absorbent side on the wound by mistake, which would be useless for wound care.