Lieberman and Mengele fight, and Lieberman and a dog get shot. Afterwards there is no blood on the carpet. Only after Lieberman collapses on top of the mauled body of Mengele is there suddenly blood on the carpet.
Barry Kohler (the character played by Steve Guttenberg) suffers from wardrobe discontinuity errors all through the opening scenes (which all seem to take place on the same day, as he follows the bad guys from the outdoor cafe to various spots including the airport with his camera). He is at first wearing a blue-yellow plaid shirt with a white t-shirt underneath, then later wearing a shirt with no t-shirt underneath, and still later the white t-shirt by itself, with the outer shirt gone. Also, when he is wearing an outer shirt, the color changes, first to what looks like a blue denim, and later to a red-blue plaid.
Shortly before the first assassination you see the victim taking a leak. Over him are two signs. On closer look you'll notice that they both list Austrian Addresses. Like the scene moments earlier this was also shot in Austria and not in Gladbeck/Germany.
In the movie, the young clones of Hitler all have dark hair. However, in real life his hair was never dark. As a young boy he was blonde, and his hair became medium brown as he got older, as is the case with many blonde children.
The theory of replicating a clones upbringing and environment, in reality, could never come to fruition because all the circumstances and events could never be replicated. For instance, replicating the death of the cloned Hitler at age 65 is possible, but the other events that contributed to Hitler's psyche, such as his experience in WW I, to include him leaving his native country, in his case Austria, to join another countries army, Germany, to fighting in the trenches, suffering from mustard gas attack, to being discharged from a defeated nations army and into a depression where a wheel barrel full of money would buy a loaf of bread, to ultimately facing the threat of communism within his own country, to forming political resistance against it, to being imprisoned for his failed attempt at it, etc... could all never be duplicated in order to shape the cloned Hitler into the mindset of the original one.
The goof items below may give away important plot points.
The central point of the film is that as well as being exact genetic clones of Adolf Hitler the "boys" must also grow up in a similar environment, therefor the older father who dies at 65 etc., but Hitler was the fourth of six children, three of whom died in childhood, the boys are all only children.
Near the end of the movie (approx 1:56:28), as Bobby Wheelock sends the remaining dogs out of the room and says, "Out!", the dead dog (who has been motionless on the floor for most of the scene) picks up his head and twitches his ears then puts his head back down.