(at around 1h 25 mins) When Johnny intercepts the laser it is aimed at a New York skyscraper. However, when he detonates the final cataclysmic blast, he appears to be in orbit.
(at around 1h 25 mins) Laser beams continue moving in the direction they are aimed. Dr Doom's laser cannon was aimed at an upward angle, and would simply continue into space, not descending on New York, as shown in the film.
When Reed Richards 'stretches' his leg to trip up Doom's henchmen, the trouser leg of his yellow PPE suit is somehow still covering it.
(at around 1h 21 mins) The laser has fired before Johnny can even say "Flame On", and minutes pass before the laser reaches New York. But as a laser, the beam should be moving at the speed of light, which means Johnny should not be able to intercept it.
The diamond is obviously a prop made of plastic resin. A diamond (or glass copy) of that size should weigh several pounds yet the Jeweller easily lifts both the real diamond and the (presumably glass) fake with one hand when swapping them over.
(at around 39 mins) One of the jeweler's minions sprays Alicia in the face with a spray to knock her out. We see a Point Of View shot from Alicia's point of view showing her being sprayed and her head nodding. However, Alicia is blind so she should not have a point of view.
(at around 1h 15 mins) Following the Fantastic Four's escape from Dr. Doom's captivity, they arrive back in the city. Even though no time at all has passed since them, they now apparently have their own building with a "Number Four" logo on the side and an aerial transport vehicle. They did not have time to put their logo on the building or build/acquire the vehicle.
The Human Torch is apparently able to control his fire powers while they are stranded in the woods following the shuttle crash. Yet when he accidentally activates the power when he is with the doctor, he freaks out.