Tintin/WMG

Tintin is an orphan with no surviving relatives.
Pretty much explains why, up until moving to Marlinspike, he's always on his own despite just being a teenager.

Going with the orphan theory, Tintin's feats inspired Watari to open up Whammy House in order to find and nurture more geniuses who might otherwise go undiscovered.

 * Hmmm... Although Tintin looks much, much more normal than the kids raised in the Whammy House.

Tintin's father is Indiana Jones.

 * Maybe Indy had a relationship with a woman in Belgium, left the mother, but the adventuring gene is very strong.
 * And he'll make a cameo in the next film. Most likely wishful thinking, but...

Tintin's father is Henry Jones Sr.

 * Given the time period Tintin was first published, Indiana Jones may have been too young to father him. His father, however...

All the main characters and some of the recurring characters are Immortals
Specifically, Tintin, Haddock, Calculus, the Thom(p)sons, Rastapopulos, Allan, Alcazar, Tapioca and some of the others (possibly Abdullah is Not Allowed to Grow Up).

This explains why they don't age and the occasional Made of Iron or No One Could Survive That moment. The series basically depicts the never-ending struggles of a small clique of immortals through the 20th Century. For some reason, in this universe the fact that an immortal can be killed by decapitation is not widely known even among themselves. (This means that about the only time Tintin was actually in danger of dying was in The Blue Lotus.)

All the main characters and some of the recurring characters have time travelled at some point.
Tintin's first adventures take place in the 30s (japanese invasion of China, Al Capone, the Chaco war, etc.) The later adventures take place in the second half of the century (the Cold War, exploration of the Moon, etc.), with the characters apparently having neither aged nor lived through WWII. The aliens from Flight 714 must have abducted them before WWII and brought them back to Earth in the 60s, unaged thanks to relativity. They don't remember it of course because their memories were erased by hypnosis. This also explain why Kanrokitoff just happened to be there on the island when they landed. The aliens must have been monitoring them. Perhaps they saw a special purpose for them in the later 20th century and that's why they brought them forward in time (perhaps at the same time saving them from dying in WWII).

Tintin is a Time Lord.
Think about it: He doesn't age. He has no relatives. He talks to animals. He has no interest in human females. Maybe his TARDIS malfunctioned and had to occupy a white fox terrier! Just like the Doctor's TARDIS malfuntioned and had to occupy a woman.
 * He also makes a point of helping everyone he meets, dislikes injustice, loves to travel, wears a long coat, and makes close, lifelong friendships with eccentric-but-endearing characters. And has had Moffat on the writing team.

The Incas from The Seven Crystal Balls/Prisoners of the Sun had in a Dark Age ever since the conquistadores.
Among other things, they had forgotten what their ancestors knew about astronomy.

Frank Wolff isn't dead.
When he he was instantly teleported into  Remember, they have been observing Earth for years, so they'd probably want to keep an eye on the Syldavian's space program. When they realized what Wolff was up to, they intervened and saved his life.

The phostlite radiation from the Shooting Star turned Tintin immortal.
It also made him radiate a mental block that makes people not notice or care that he's been around forever. Both effects are uncontrollably passed on to those he particularly cares about or spends a lot of time around, though secondary immortals aren't contagious.

At some point in the next movie that Tintin meme will be mentioned.
The one where Haddock goes 'HA HA HA, OH WOW' to be exact.

The Bordurians are real life (in universe) Commie Nazis
While the events of The Calculus Affair are set during the Cold War and Borduria uses quite a few Commie Land tropes it also still has a lot Nazi/Fascist elements - in fact the political ideology of the ruling regime is called 'Taschism', after the dictator Marshal Kûrvi-Tasch.

Professor Calculus knows he is deaf and doesn't use a hearing aid on purpose.
Calculus is quick to anger, like Captain Haddock. Unlike the captain, however, Calculus is remarkably violent. Watch how he acts during "Destination Moon" and "Explorers on the Moon." He assaults several people and goes on a rampage after the captain tells him he's "Acting the goat." Calculus also has no problem yelling at the Twins when they question his authority. He also beats the crap out of Carreidas in "Flight 714."

Calculus is aware that he has serious anger issues. While he has trouble controlling his temper, Calculus uses his deafness to hide it. Because he cannot hear people correctly, Calculus just assumes that they are not trying to anger him, and this keeps him from losing his cool.

In the film, Nestor knew about Sir Francis' puzzle and the location of the treasure the entire time.
It seems that Nestor had been working for the Haddocks his entire life, seeing as how he had served the Haddocks before Marlinspike Hall was sold off. It's also implied that his entire family served the Haddocks, since Sir Francis' first mate resembles Nestor. Finally, Nestor seemed to have some knowledge about the clues Sir Francis left behind, since he subtly gave Tintin a crucial clue to the importance of the model Unicorns. However, being the loyal retainer that he is, he was just biding his time until a Haddock returned to take possession of Marlinspike Hall.

The next movie will pick up with the rest of Red Rackham's Treasure and somehow incorporate The Calculus Affair.
The film leads off with Tintin and Haddock agreeing to find the treasure, so that's where it will pick up. Professor Calculus will be introduced and stay important throughout the entire film, but will only be minorly in-focus compared to Tintin and Haddock. I wouldn't doubt Bianca or Allan popping up again, but we might have to wait for a third film to see Rastapoulos.