Continuity mistake: The license plate's number of Indy's Tuk Tuk changes from 4717 to 1132 in a few shots during the Tuk Tuk Chase.
Continuity mistake: While Indy is fighting Colonel Weber on the roof of the train, Basil is pointing a pistol at them, and his grip on the pistol changes from a two-handed grip to a wrist-stabilizing grip as the shots change.
Factual error: When Indy wakes up on the day of New York City's parade for the Apollo 11 astronauts, H.R. Pufnstuf is on the television. The parade was held August 13, 1969, but H.R. Pufnstuf didn't premiere until September 6, 1969.
Continuity mistake: When the soldiers bring Indy to Weber, in the background Voller and the two soldiers with the lance can be spotted already leaving. After Weber finishes interrogating Indy, Voller and the soldiers are back in their original places with the lance.
Character mistake: In the plane, Mason says that Voller's associates killed three American civilians. But they only killed two: Mandy and Plimpton.
Continuity mistake: During the conversation in the Tuk-Tuk, Helena's right arm continuously goes from being down to grabbing the roof of the Tuk-Tuk between shots.

Continuity mistake: Weber commands a soldier to open the Lance's box. In the shot of the soldier's hands, a ring has appeared on his left hand. This ring disappears again when Weber says "Doctor."
Continuity mistake: When Indy horseback rides on the subway platform, the people stand behind the columns. A shot later from the opposite angle, they're all standing in the middle of the platform.

Continuity mistake: In the college archive, Indy opens the cardboard box. In the close-up he opens it again.

Continuity mistake: When the waiter arrives at the room where the Nazis are, all the papers and books on the table, plus the pencils, change positions between shots.
Continuity mistake: When Renaldo gives instructions on diving, he holds several cables. From the shot from behind, he is grabbing them close to a tape that holds them together. Shot changes and the grip differs, and the tape is gone.
Revealing mistake: During the parade, after the red convertible skids, Indy's horse rears. When it turns around, check Indy's face and you'll notice that it's Harrison Ford's stunt.

Continuity mistake: Indy tries to make a phone call but is abducted by the baddies. There's a close-up of the phone and blood has suddenly appeared all over it.
Continuity mistake: When Helena is doing the magic tricks, Renaldo reaches for the cards with both hands. Shot changes, and he is reaching just with one.
Continuity mistake: Before the tuk tuk comes to a stop, a man in a blue djellabah is walking by next to it. When the tuk tuk stops, the man is suddenly 3 meters behind, repeating all previous movements.

Factual error: The crown on the logo of the Air Maroc plane is the modern 2013 version, not the one from 1969 when the movie is set.

Continuity mistake: Indy stops Basil from hammering the dial and makes the left side of his jacket open to reveal his shirt. Shot changes, and now the opening has swapped sides.

Continuity mistake: Indy horseback rides past a truck with a flag, then between a dozen of musicians while chased by a motorbike. When he looks behind him, the band has vanished and the truck is next to him again. This last shot belonged in the first place.
Continuity mistake: Before Indy jumps on the horse during the parade, a man in a plaid shirt runs away. Shot changes, and he is back in the previous position, yet he is now walking slightly faster.
Answer: It was never explained and seems impossible that anyone could survive such an impact. My own thought was the scene was deliberately exaggerated to appear as if Voller was killed in order to fool and then surprise the audience when he later turns up alive. I also thought it looked as if he hadn't aged. Voller may have been much younger than Indy, possibly as much as 25-30 years. When Voller reappears in the 1960s, he looks more like actor Mads Mikkelsen's actual age. The film should have made him look younger at the beginning. There's a lot of "suspension of disbelief" here.
raywest ★
It is also possible that he underwent facial surgery after surviving this.