When Valerian gets the 'Update' when they arrive at Alpha, Alex says that since leaving Earth the station has traveled almost 700 million miles (7.5AU), which, if true, would mean that in 400+ years they hadn't even reached the orbit of Saturn yet (which is 9.5AU from the sun), something that probes can do in under 10 years. A good example is Voyager 1, which in 40 years has traveled over 12 BILLION miles from Earth and is now in interstellar space.
The station is moved away from Earth because its gravity is having an effect. The only effect it could have is a tidal effect, and this seems unlikely given its relatively small size compared to the moon. Putting it into an orbit round the moon would be an easy fix since the combined mass would be only negligibly larger. Another easy fix would be to move to a new location at the L2 or L3 Lagrange points (L2=behind the moon, L3=opposite the Earth [behind the sun]) and drop a satellite at the L3 or L4 points to retain contact with Earth. (The Lagrange points are where gravity effects cancel each other out in a 2 body system [Earth/Moon, Sun/planet, etc])
In Big Market, Valerian lures the weighted metal balls onto a thug's body, who then crashes through the floor. When Valerian is chased out moments later, the hole in the floor is gone.
As they are leaving the big market planet Laureline says "Leaving Exospace in 5 seconds" when it should be Entering.
When Valerian and Laureline are talking. Laureline is not wearing a safety harness, but on the next shot,she is. Cut back to Valerian, and she isn't. They then put on the safety harness she was already wearing.
When Alpha is initially boosted from Earth's orbit, the detachable rockets propel the station in the opposite direction of Earth. However, in order to leave orbit, it is necessary to propel the station in the same direction as it is traveling in its orbit, parallel to Earth.
In Commander Filitt's office, the plaque in the background showing all nation flags in the United Human Federation contains at least one duplicate (in the case of Japan) and most four (in the case of USA) or more.
In the opening scene of the movie an American Apollo and Russian Soyuz craft link up. The distance shot is of the correct two craft but the docking footage is actually from an Apollo command module looking at an Apollo lunar module.
Valerian, Laureline, and Bubble crash into a hallway from a trash chute. In the trash are skulls. The horns on one of the skulls flop around as Valerian gets up.
Planets are identified as being in a 'Constellation' followed by a three digit code. Constellations are patches of sky as viewed from Earth. They contain unrelated stars and galaxies.
Having 'sectors' as in Star Trek would make much more sense.
General Okto-Bar pronounces the name of the planet Mül several different ways.
When Sergeant Laureline finds Major Valerian after the chase she comes to an edge of sulfur shaft. Her toes are over the edge in the next shot she is about 10 centimeters away from the edge.
Bubble Dance - whip scene. Rihanna whips the glass and from it the lemon umbrella and the starfruit falls. In the next scene, the starfruit reappears on the glass.
At the end when Valerian says "I want only your name on my playlist" his mouth movements don't match the dialogue.