When The Doctor confronts the Nina server on the stairs in Clara's house, in shots where she is facing The Doctor, from his point of view, she is holding the handrail with her right hand. In shots from the side of the staircase, she is standing backwards, away from him, with her left hand next to the staircase.
In one scene when the doctor leaves the Tardis on a motorcycle the Tardis's doors are open. In the next scene, which is just a pan out from the previous one, they are closed. The doctor did not do anything to cause this.
When The Doctor and Clara was inside the cockpit of the crashing plane, aside from the glaringly obvious absence of warning bells and voice prompts, the pilots were sitting in the wrong side. It was showing the Captain (4 bars on his shoulders) sitting in the right hand seat (facing the windscreen), which is usually occupied by the First Officer. It is against company protocol for pilots to sit in the wrong seats.
When The Doctor and Clara burst into cockpit of the falling plane, the subsequent shot shows the plane with undercarriage retracted. On the cockpit panel, however, the lights signal "gear down and locked" position (all green). Furthermore the primary flight display displays no artificial horizon at all. Also, there would be a cacophony of aural warnings like "Terrain!" and "Pull up!", given the plane is about to crash.
Clara was shown to have made herself a cup of tea when she went outside to The Doctor after she woke up from her near upload. But the cup she was holding was clearly empty as she was pulled into the TARDIS, and tumbled around on board a crashing plane and yet not spilled a drop.
While The Doctor and Clara are riding around London on the Triumph, you can see the camera reflected in their helmets.