When Pippi hurls the giant snowball towards the burglars, the sky alters between sunny, overcast, and twilight.
When the policemen sit down to clean their faces after being hit in the face with pies, there is far more meringue and cream on their faces than in the previous shots.
The snakes that Paula handles are boa constrictors and therefore not venomous as the MC seems to think. This could be explained by the public's general lack of knowledge about snakes at the time - the circus would have counted on the audience not knowing this fact and being impressed.
It is apparent that Pippi has superhuman strength. But Tommy and Annika, who do not, still have no trouble lifting her full case of gold.