Goofs

The planet Melancholia disrupts all electricity in and around the house, including the electrical systems in the cars in the driveway. However, Claire is able to jump in an electric golf cart and drive away with no problem.

When John throws Gaby's things out, he does so onto the middle of the steps, but when the house keeper comes out to take them they're on the right side of the steps.

When Claire is putting Justine in the bed, Justine is placed in the bed asleep facing away from the door. In the next shot she is facing the door. Then away from the door, and again back to the door. She is asleep the entire time.

One cannot view the same constellation (Scorpius) at the same location in the celestial sky from late evening to early morning due to the Earth's rotation.

There is no reason for Melancholia to cause electricity problems on earth. However, its gravitational pull would have caused earthquakes and volcanic eruptions due to tidal forces. These would have been globally destructive long before any actual collision.

During the fly-by, Melancholia is shown to become apparently smaller by more than 5% (diameter) in 5 minutes, when traveling at a known speed. Calculation shows that it is roughly 5 earth radii away. It should have taken up large portions of the sky at this distance (more like what is shown at the end of the movie) and would have had catastrophic effects on the earth, even if only flying by.

The picture of the interactions between both planet orbits taken from internet shows only the trajectory of the fly-by planet changes because of the gravitational forces and there's no effect on the earth orbit. According to the laws of physics it is wrong. Both planets trajectories should be affected, the lighter planet trajectory would get affected the most.

When Melancholia rises in the evening, it is seen almost as a circle. The lower part is missing, thus indicating that Melancholia is lit from above which would make it day at the part of the Earth from which we are watching.

John mentions numerous times that there are 18 holes on the golf course, but when Claire is rushing out with her son during the hail storm a flag is shown behind her with number 19. However, the 19th Hole is what most bars at the end of a course is called and is typical of a lot of golf courses. It's not a literal "19th hole" ... just what the bar is named. The symbolism here being that humanity is at the end of the course.

Some say that the planet Melancholia could not possibly be in full phase at all times, because you wouldn't see the planet in the sky during the day. However, phase is a matter of relative position of a planet (or other celestial object) relative to earth. Daytime sunlight obviously drowns out the light reflected from a planet. But just because you can't see it doesn't mean the planet is not in full phase.

The license plates on the vehicles in the film are from the US State of Pennsylvania. When looking out over the golf course, you see islands in a vast sea, there is no such location in the State of Pennsylvania assuming that is the setting.