This movie seems to imply that the Wakandans had exclusive access to vibranium only until Klaue stole some of the supply. Howard Stark had a small sample of vibranium decades before Klaue stole his portion (which is what made up Captain America's shield), yet there is no explanation as to how Stark got his sample.
When Killmonger and T'chala are arguing in the middle of their fight by the train, the sonic dampeners are active yet when they resume fighting their masks activate. This shouldn't happen since the vibranium should be inactive.
M'Baku says his tribe are Vegetarians, but then says that T'Challa's body was discovered by one of his tribe's fisherman. However, fishing could have other purposes besides obtaining meat (such as fish farming).
When Shuri gives T'challa the new shoes (called sneakers), she mentions that they absorb sound & allow silent footsteps, which T'challa demonstrates. Later in the film, T'challa runs up a ramp wearing the sneakers... accompanied by the sound of footsteps.
When T'Challa is addressing the UN, a Welsh flag can be seen among the other flags in the background.
As a part of the United Kingdom, Wales doesn't have UN membership in its own right, so this flag would not be displayed.
One Wakandan subtitle has a misspelled word: "descendant" appears as "descendent".
Killmonger is said to have "graduated from Annapolis at 19". Annapolis refers to the United States Naval Academy in Annapolis, Maryland. They do not allow anyone younger than 17 to enroll, nor can you graduate early due to its rigid four-year academic program for its midshipmen.
Since Wakanda is a landlocked African country hidden due to their technological advancements and isolated from the rest of the world, and since it was implied that Erik Killmonger, despite having Wakandan heritage, was raised in the United States for most of his life; it doesn't make sense how Killmonger could have perfectly navigated his way to Wakanda by airplane - from South Korea, no less.
When Everett K. Ross enters the interrogation room he has the listening device on his left shoulder. When he leaves the interrogation room, it has vanished. But when the scene cuts to a different camera angle, you can see the listening device again (it is out of focus though).
During the scene where Ulysses Klaue is being interrogated by Everett Ross, you continue to hear Klaue speak whilst the camera is shown outside the interrogation room, with the camera focused on T'Challa. When T'Challa begins to walk, you can see Klaue behind him and whilst you can hear him still talking, his lips aren't moving within the interrogation room in the background.