Too many errors about nuclear reactors to list.
Palm trees in Cleveland, Ohio.
The shape of Howard's head changes throughout the movie, depending on whether he's being portrayed by an actor in a suit, or as an animatronic puppet (his head is larger to accommodate the actor inside the suit when it's done that way; his head is narrower when it's just a puppet).
In the diner scene, a truck driver grabs the key card from Howard and asks "What's this, the key to your duck mobile?" Howard never mentions that it is a key and it being a high-tech gadget, does not resemble a key in any way (especially not to a Mid-'80s truck driver).
In the diner scene, when Howard is levitated and spun around near the ceiling by Dr. Jenning, the shadow reveals a pole reaching from the ceiling to Howard to achieve this effect.
When Beverly is in Howard's wallet the cash still says Washington DC on it.
Beverly's umbrella disappears from and re-appears in her bag when she first meets Howard.
(at around 1h 11 mins) During the diner scene when the Overlord levitates and begins spinning Howard, the rope was edited out, but the shadow of the rope used to suspend the actor is still visible.
During the diner scene when Dr. Walter Jenning (while being the Dark Lord) sends the man through the window with his energy and the guy lands on a car, you can see that a wire that is attached to the guy.
During the final scene, in which Beverly's band is playing on stage, there is a mirror as part of the stage in which the crew and camera can be seen occasionally.
When Howard and Beverly try to exit the diner, the dark overlord prevents them leaving. When he closes the door and moves the plants, and then shoves the furniture in front of the door, you can see thin ropes stretched from the door and across the room. These guide the furniture towards the door.
When the cops are chasing the microlight, two police cars jump a hill crest. Ramps are visible when the cars drive over them.
When Phill is driving Beverly, Howard and Carter in a van to the lab, the shifter for the van is in the Park position.
When Howard is in Beverly's apartment for the second time he starts a rhythm and bass sequence on one of the gadgets in the apartment to play along with. The machine that produces the rhythm and bass is actually a Roland TR-707 Rhythm Composer which produces a different kind of drum sound (more electronic) and can't produce any bass sounds at all. It is also not capable of sending out MIDI data to drive external equipment like the synthesizer in the apartment to produce the bass sound.