Since this serial deals with an alternate history which diverged from our timeline in 1916, most so-called anachronisms and factual errors (weaponry, design, uniforms, etc.) dealing with events from that point on should be regarded as plot holes at best, and redundant at least.
When Tucker is in the storage closet, the outlet has the modern three plug sockets. While grounded outlets were not mandated until 1969, they were first introduced in 1926. It is not inconceivable that a government building would have them in the 1940s. In addition, this serial is set in an alternate history which diverged in 1916.
As the Germans are shooting at Archer and Silik they hit 55 gallon drums multiple times, there are many sparks upon their impact, but there are not any dents or holes left in the drums.
As the insurgents are fighting the Germans, none of their guns are producing a muzzle flash consistent with the firing of bullets.
When the Resistance fighters attack the Nazi facility to distract the guards none of the actions on their pistols cycle when fired, and the hammers are always in the upward uncocked position, which they wouldn't be if the gun had just been fired. A 1911 is a single action pistol, it cannot fire with the hammer up, and each time the gun fires and the action cycles the slide moves the hammer into the downward cocked position.
When Archer tries to contact Enterprise and fails, Silik says it's because Enterprise is in the Earth's atmosphere and the ionisation is preventing his com signal from getting through. This is nonsense. Earth's atmosphere could never block a Starfleet com signal.
When Archer and company are fighting the Germans at Vosk's facility in New York, Enterprise is seen approaching the East Coast from orbit. As seen from orbit New York is already seeing the sunrise, but on the ground it is still completely dark.
Reed reports that in the altered history, Russia remained neutral, so the alien-backed Nazis only expanded westward. Yet in Storm Front (2004), the German General told Vosk that Germany's forces are strained because the Russians are attempting to retake Moscow.
Archer suggests Silik needs Enterprise to send the information gained about time travel technology into the future, but that is not true. Time travels forward all on its own. All Silik would have needed to do is bury a few discs somewhere safe on Earth. Then, his employer could have another recruit dig one of them up at an opportune moment later in time.
Malcolm says that in the Nazis have taken England. He should have said Britain. England and Scotland do not have their own individual armed forces. As a Briton with a proud Royal Naval heritage, Malcolm would have known this.
When Carmine confronts Alicia about the communicator he found in her jacket, he says it looked like the thing Archer took off 'those Martians'. In fact, the two props look very different and a mind raised in the early 20th century would not have made that connection.