When Hackerman is hacking Kung Fury back in time, he points his right hand with the Power Glove at the monitor and shoots a beam. Then it cuts to the wide shot, he is still pointing his right hand at the screen. When he stands, you clearly see the Power Glove on his left hand. If you look at his shirt, the E is backwards, indicating this scene was mirrored in post-production.
To send Kung Fury back in time Hackerman presses the 'Break' key on his computer. Pressing the 'Break' key on 1980s computers would normally interrupt a program's operation.
At 10:30 Hackerman tried to kinda convert equation E=m*c^2 to E=m*c^3 for hacking time. But in a line of his code he wrote "double e = Math.power( m*c , 2);" which calculates m^2*c^2, not m*c^2. However, this mistake is the reason why he hacked too much time.
Though set in 1985, while fighting the evil arcade machine, Kung Fury was thrown out into outer space and hit the Hubble Space Telescope, which was launched in 1990.
On the screen of the hacker the line System.out.println() is shown several times which is Java code. Java did not exist until 1995.
In the precinct scene, the Police Chief mentions Viagra. Pfizer did not patent Viagra until 1996.