Continuity mistake: When Kristen Wiig is bringing coffee to the office building and meets Walter Mitty reviewing negatives, her purse changes shoulders. When the camera is on her the shoulder strap is on her left, but when the angle changes to her back facing Walter the purse is visible and hanging off her right shoulder.
Other mistake: When Sean Penn is about to let Ben Stiller look through his camera at the 'Ghost Cat' he bumps the camera. They are very far away from the animal and any bump of the camera would A) be immediately noticed by the worlds best photographer and B) move the subject very far out of frame.
Continuity mistake: In the scene where Walter is bribing the Warlords with cake, the warlord stabs the cake with his bayonet through the lemon icing wedge, but in the next shot the knife is in at a different angle when he takes a bite. Then as he he smiles at his men the knife is inserted into the cake in a completely different way, with no bite missing.