The night before Steve and Karen's wedding after Steve decides to let his mum invite Ken and Deidre, she walks out the front door, straight past the Barlows. Then, after they finish their dialog about Tracy, she comes out of the toilet.
In the episode, 22/11/2004, (where Dev's corner shops are blown up by Maya) Dev drives his Saab to the shop which is about to be blown up, he parks the car directly outside the shop. Also parked directly outside the shop is another car. As the shop blows up, the camera changes angle to show the blast and Dev's car has somehow disappeared, just leaving the other car in shot.
In the episode after Katie kills Tommy, the expression on Tommy's face keeps changing throughout the episode.
Due to being a long running soap opera characters history's and backstories are retconned and certain plot points are forgotten i.e. characters celebrating their birthdays on the wrong days or forgetting about key details in their lives.
In the episode where Candice is going out with Vik, he gives her a ride home. You can clearly see the reflection of a cameraman, his camera and microphone in the mirror.
When Steve punched Michelle's stalker, you could see the punch didn't connect on a shadow on the wall.