Early in the film, some of the characters are playing a trivia game and two of them "high-five" each other. The "high-five" didn't begin until the late 1970s and wasn't popularized until the early 1980s-by athletes. In 1966, athletes would simply shake hands.
The characters frequently use vernacular that was not made popular until much later than 1966. Characters refer to protection as 'condoms,' which were much more commonly called 'Johnnies' in the 60s. Also, Young Carl is told that when dealing with Thick Kevin, it was important to "think outside the box," a term not coined in general use until the early 90s.
The silver turntables with the slim straight arms used by the DJs and the tape reels didn't come along until much later - maybe 20 years later in the case of the turntables. (Odd that they were used because they also showed clunkier Garrard turntables that appear to have been correctly from the 1960s.)
Early in the film, during the trivia game, one of the characters guesses "Jimi Hendrix," though this is set in 1966. Jimi Hendrix moved to England in mid-1966, but didn't release his first single until 1967, which is when his fame began.
Angus tells Carl about every second Saturday, where each DJ is allowed to invite one girl onto the boat. He then asks Carl who he will be inviting onto the boat, though Carl is not a DJ.
Then the Count is also seen with twins, breaking the one girl rule. And Harold, the producer seen for a lot of the shows, is seen greeting a girl.
In the Christmas scene at the government minister's house, the minister's daughter offers Twatt a mince pie. A mince pie can be clearly seen already on his plate and when he accepts the (apparently second) the other has vanished.
In one scene, some of the DJs are clinging to the rail on the deck of the sinking ship to keep from sliding down the deck. In a later scene, three of the DJs are standing upright in the studio and not leaning like they would be if the ship were sinking at a 45 degree angle. Also, the water in the studio is level as if the ship were sinking levelly.
In one scene Quentin goes to young Karl's cabin to tell him his (Karl's) mother is coming on board to visit. It's apparent in the shots of Quentin the ship is rocking, but in the shots of young Karl you can see the horizon through the porthole behind him, and it's not moving. This should be noticeable if the ship's rocking as obviously as it is in the shots of Quentin.
In one scene, two characters are speaking in one compartment of the ship. Lights hanging from the ceiling are noticeably rocking, because of the motion of the ship in large waves. The two characters move to an adjacent compartment of the ship, in which a rousing game of foosball is underway. Presumably, a game of foosball on a ship rocking in a heavy seaway would be futile.
When they start the final record by Procol Harum, we watch a single at 33rpm. That is possible as it was a very long track. Nevertheless when we have a second view of the turntable a few shots layer, it obviously plays at 45rpm.
When young Karl goes to the broadcast studio to ask Bob about being his Dad, the clock on the wall reads 3:20 (AM) when he arrives. A conversation ensues during which Bob finishes one song, then introduces and starts another as he talks with Karl. But when the scene ends after several minutes, the clock still reads 3:20.
In the first aerial shot after the Radio Rock ship goes "on the move", the exhaust from the ship's stack is blowing toward the bow (forward), but in the next and subsequent shots it's blowing toward the stern (rearward).
In the Christmas dinner scene, when Dave is giving his toast to Carl and the camera cuts to Quentin, a cameraman is clearly visible in the background, in the top right corner of the screen, wearing a black t-shirt, holding the camera.
The Boat is sinking at a position given as 53 degrees 17 minutes North and 2 degrees 15 minutes East - which is a position 70 km Northeast of Bacton in Norfolk, (the nearest town on land) - however Gavin is requesting anybody with a boat in Suffolk to help with the rescue. Suffolk is a long way to the South and he would do better to ask for help from anyone in Norfolk.
Smooth Bob gives a message for Carl to tell his mother that "Muddy Waters Rocks" and vocalizes the familiar riff from "Mannish Boy", Waters's 1955 hit song. When Carl gives this message to his mother she mistakes it for Bob revealing to Carl that he is his father, meaning the song or Waters must have reference to Carl's conception in some way. As the film is set in 1966 and Carl is 18, this would place that moment at at least 1948, long before his fame and seven years before "Mannish Boy" was released.
Simon's wedding to Elenore was not legitimate. Contrary to belief a ship's Captain cannot marry anyone unless he is a minister, a magistrate or a judge. Even if a Captain could perform marriages at sea, the wedding still wouldn't be legal as Quentin was the one officiating at it, he was not the Captain of the vessel.
When the crew are huddled at the stern of the ship near the end, it is pitch black. Within minutes the fans' boats arrive to rescue them, and the sun is now over thirty degrees above the horizon (about 9 a.m. at that latitude) with enough light to read the welcoming signs which were illogically created to impress the crew. The sun cannot rise that fast.