Red is supposedly a black belt in Karate (Granny has a picture of Red winning a trophy), but when she fights Boingo in his lair, all of her blows are directed at his head, which is easily defensible due to the rabbit's prehensile ears. Red should know that when attacking a shorter opponent, you use your reach, and strike vulnerable spots. Instead, she continually launches blows that are easily blocked.
After drinking Granny's coffee, Twitchy becomes supercharged and races down the mountain. But coffee is not a stimulant. Caffeine inhibits the adenosine in the brain, which "tells" the body it is tired. Caffeine essentially tricks the body into thinking it isn't weary. After drinking the coffee, Twitchy might be more alert, but he wouldn't have any extra energy.
Wolf tells Twitchy to remove the flash from the camera as the job is "covert", which he does saying, "Okay no flash!". However, later, when Red falls out of the cable car, the flash is back on the camera.
Nobody knows where the coffee came from when Twitchy drank. Before that, everyone is sitting around in Granny's cottage and no one is drinking -- no coffee mugs in sight. Then, as soon as they're outside, Granny has a coffee mug in her hand.
In the end credits, the voice actors' names (in 3D block letters) are lit by a spotlight. As the light pans either right or left, the shadows of the letters go the same direction. They should go the opposite direction.
Even though many differences in the four main characters' retelling of the story exist (object positions, lighting, and even dialogue), they aren't continuity errors, but the movie's actual representation of differences in their stories, just as real-life eyewitness accounts do indeed differ. Example 1: in Red's variant of her second run-in with the Wolf, we only see her spray him with "Wolf-Away" (a parody of many repellents) and then takes off, yet when the Wolf retells the same scene, she not only sprays him but she also beats him up. Example 2: Granny's equipment is slightly different in different scenes where Red saw her in the sky. Example 3: Japeth's whereabouts during the mineshaft chase vary between the stories.
When Wolf is tossing the dynamite out of the mine car, it is still in the tunnel. While the dynamite tossed on the open-air track detonates, the tunnel is still intact a moment later when Japeth and Red fly out. The tunnel should have been blasted shut.