Factual error: When J.J. first discovers his powers and understands math, the parabola "seen" on the board is wrong for the given equation and it's different than what J.J. actually ends up drawing, which seems more like the right answer.
Continuity mistake: When Stephanie falls while running, the tears in her jacket change. As she's rolling, you see a big tear in the left shoulder, and when she stops rolling you see the left sleeve has no holes or tears. When it cuts back and she's still on the ground, the left sleeve has several tears and the big one on the shoulder is missing.
Continuity mistake: When the girls run into Olivia and Mr. Robbins, the positions of the coffee cups on the table change.
Continuity mistake: When J.J. and his grandpa are talking about Jim while playing pool, the way J.J. holds his cue stick changes throughout the scene.
Continuity mistake: When Stephanie runs in and sees 'Jim' on the floor there is a huge puddle of blood on the floor. When 'Jim' changes back into Amelia the puddle disappears.
Continuity mistake: When Jim knocks George down and asks if he's OK, George is lying on the ground. In the next shot, he's on his knees.
No Ordinary Beginning - S1-E20
Continuity mistake: When Katie picks up her baby, the blanket isn't around the baby's head and her hand is directly against the head. In the next shot, the blanket is over the baby's head so Katie's hand is touching the blanket. It switches back and forth depending on the angle.
No Ordinary Beginning - S1-E20
Continuity mistake: When Ben (the electricity powers guy) collapses after getting hit by his own electricity blast, he's somewhat parallel to the wall and not touching it. When Jim rushes up to him, his hand is lying up against the wall. In the next shot, he's now almost perpendicular to the wall, with his neck and shoulders lying against it. In the next shot, he's about an inch away from the wall and not touching it at all.