The scene where a man is hanging from the balcony of a large block of flats was filmed on the Heygate estate in London. Work on this estate did not begin until around 1970 and the estate was not complete until 1974. Even then, it would have taken another year or two to populate the estate. There is a similar estate just down the road called the Aylesbury, but that wasn't completed until much later.
There is a scene where the two main actors are running around the corridors of a block of flats leading to a scene in one of the flats leading to a beating. These flats are on the Bloomsbury Estate in London. The scene is set around 1969, the estate was built in 1972/3, so wouldn't have been there.
The two actors who play the "gangster" at the two points in his life are 7 inches different in height. When paired with the older versions of the same character later in life, there are few if any scenes when Malcolm McDowell (the shorter actor) is standing beside them. Surprisingly, they did not attempt the old Hollywood box or trench technique.
The goof items below may give away important plot points.
Exactly an hour into the film, the young Gangster states that he is carrying a "Beretta" on his way to kill Lennie. It is actually a Browning P-35 "Hi-Power," the same weapon he has carried throughout the movie.
When Gangster 55 is telling Freddy Mays to shoot him and the camera is showing his back you can see the gun that Freddy is holding on the couch. The next shot Freddy Mays puts the gun on the couch and leaves.