Factual error: When the shuttles are approaching the station, their engines are firing from the rear, meaning they are in constant acceleration toward the station. When arriving at a station, you would need to slow down as you approach, meaning the engines should be firing forward (or the shuttle should reverse direction). This happens in all scenes where shuttles are approaching the station.
Factual error: When the Armadyne computer reboots, you can see the typical bootup screen which gives away certain information about the computer: In two consecutive shots of the screen, you can see that this computer has a BIOS, a GA-MA790XT-UD4P mainboard from Gigabyte, 4 gigabytes of RAM, and apparently works with IDE drives. The successor to the BIOS is called UEFI, the mainboard and 4 GB of RAM are only remotely up to date as of 2014, and IDE drives are already dying out in favor of SATA drives.
Plot hole: There are two plot holes in the factory that Matt Damon works in, where they build droids. There are very sophisticated droids throughout the movie performing several different tasks. So why is he working there where his job is to stamp sheet metal, attach it with bolts, and then move the droids to the oven? Surely a droid would be capable of this work, and with the factory's high level of production they would likely be able to afford a generic one for those menial tasks. Also, what is the purpose of the giant oven that irradiates everything inside? It can't be to temper or treat the metal of the droids, because then you have radioactive robots, which also means this can't be a way of charging up their batteries/ power plant. Plus they're assembled by this time, so it's irradiating the wires, hydraulics, and circuitry as well.