The film's opening shows that the Minions were originally evolved from unicellular organisms. Though, before the film, there were other widespread theories, including that the Minions were artificial creatures made out of mashed bananas, fatty acid, and mutated DNA; or changed from humans (the latter one is seen in Despicable Me: Minion Mayhem).
In the trailer, the Minions had another boss, a knight who was killed because the minions were mopping the floor and he slipped. This character doesn't appear in the film.
When the Minions arrived in the United States and the United Kingdom, there are many surroundings about people and things in 1960s, including a election poster of Richard Nixon (which reads "Finally a name you can TRUST!"), and the The Beatles doing their famous "Abbey Road" walk respectively.
The news broadcast along with many TV shows are in color. However, in 1968, the only British TV channel in color was BBC 2, which didn't show news bulletins; the other two channels of the time, BBC 1 and ITV, didn't get color until 1969.
After Kevin swallows a bomb, Scarlet intends to escape with Herb Overkill and Tim, Bob's teddy bear with her Rocket Dress. Yet, after the explosion, Kevin somehow takes back the teddy bear and it is given back to Bob.
The entrance fees shown in the Tower of London are displayed in decimal currency, but England did not adopt a decimal currency till 1971. In 1968, the currency in England was pounds, shillings and pence.
The narrator states that there's a minion called Paul, but the minion is never identified officially throughout all Despicable Me films so far.
When the minions are helping the pharaoh to build the Great Pyramid of Giza, it can be seen that the scaffolding was made out of bamboo. However, it's not possible that bamboo can exist in ancient Egypt.