In the shots of Dr. Tobel peering through his bombsight, the bomb-release switch is clearly shown as being a black Bakelite line-cord rocker switch, mounted inline on the bombsight's electrical trip-wire. Yet in the last bomb-drop shot, Dr. Tobel uses a large round push-button switch to release the bomb, and it appears to be mounted on the end of a trip-wire, not inline on the wire.
The aircraft Dr. Tobel flies aboard during the bomb sight trials changes from a Douglas Boston to a Bristol Blenheim to a Vickers Wellington.
During both of the two bomb-drops during the bomb-sight test run, the number of explosions do not match the number of bombs dropped from the bomber.
At 33 minutes Watson is shown with a lit match ready to light his pipe. The match clearly goes out with the usual puff of smoke but in the next camera angle it is fully in flame.
Professor Moriarty's name is misspelled in the end credits as "Moriarity."
The secret weapon bomb sight is a standard photographic enlarger with the bellows and lens set upside down. If it were turned on as it is set up in the movie, the light would shine brightly upwards into the bombardier's eye.
When Holmes and Watson visit the flat of Miss Eberli after Dr Tobel goes missing she says an electrician came to work on the light switch. Holmes examines the switch which is obviously of American design. A British one would have been circular and stand proud from the wall.
In the opening credits the copyright year of the film I viewed showed MCMLXXIX which is 1979. The correct year of production would have been MCMXLII (1942). [Another viewer verifies that the opening credits do correctly appear as MCMXLII]. I also noted the copyright year as differing from the release date in "Sherlock Holmes in Washington", with a copyright on the film of MCMXLII (1942), while the release date was April 30, 1943.
The "decipher the coded letters by how often letters occur in writing" would not have worked in Dr. Tobel's message, since it was "just a lot of gibberish" which substituted "following" letters for the real ones. So the letter "E" would no longer be the most prevalent letter there, nor would "T" be the next common, etc.
When the Nazi agents back up their car outside Dr Tobel's apartment at about 0:08, it strikes the sidewalk causing the row of buildings to shake, indicating it was really a large backdrop.
Immediately after the first bomb run the view through the bombsight is at ground level from the side rather than from overhead.
As Moriarty is unwrapping the Christmas present that his goons had recovered from Frederick Hoffner's workshop, it is obvious both to himself and the audience that the box is much too light to likely contain a sizable portion of Dr. Tobel's military device. Holmes would not have substituted just an empty box for the fourth section of the bomb-sight, since Moriarty's henchmen would have surely noticed how lightweight the box was and thus realized that things were probably not as they'd been led to believe, and so they would have probably scrutinized the man behind the desk to make sure he actually was Professor Hoffner, rather than their merely assuming that's who it was and trustingly bringing him to meet their boss. Holmes would surely have added a small stone or other heavy object to the box so that it would appear to still contain a section of the device.
When the doctor is demonstrating his bombsite while on a airplane, the supposed bombsite is actually an Omega D2 darkroom print enlarger. It is not upside down as another person mentioned. The doctor is peering over the top of the lamphouse where there is nothing to look through at all. Later in the movie, Sherlock is seen in his darkroom using an exact same Omega D2 model enlarger, possibly the very same enlarger.
The Nazi agent tells his partner to "leave the motor running" when they are preparing to kidnap Dr. Tobel, yet when Holmes and Tobel jump into the car a few moments later, the sound of cranking up and briefly revving the engine is heard.
When Dr. Tobel goes to see Miss Eberli, he lights a match to locate her bell and rings the bottom of three buttons. The Nazi following him then comes up after he goes inside and looks at the buttons and tells his companion it's apartment B. Since he rang the bottom of the three buttons, it would have to have been A or C depending on the order, but not B, the middle of the order.
Holmes' hand/arm/leg-movements do not match the sounds of his starting the car;, also, his and Dr. Tobel's mouths do not move during the accompanying "taking the Nazi's own car" conversation.
When they first test the bomb sight, on the first pass, both the terrain in view and the terrain where the bombs hit is clearly stock footage of bomb tests in the southern California desert.
While Holmes is in Switzerland, disguised as a book collector, he drives in a car with the steering wheel located on the right side while driving on the left side of the road. In Switzerland (and in Germany, as well, so "the Nazi's own car" would also be configured the same way), people drive cars on the right side with steering wheels mounted on the left side. The only areas of Europe where cars are right-hand-drive and occupy the left-hand lane are the British Isles and Gibraltar. A probable explanation for this apparent discrepancy is the film's overall British overtone --- the tale's primary setting is London and many of the lead actors are from England, so this is likely why British-configured cars were used.
Moriarty's men wait outside to grab Dr. Tobel when he comes back out after visiting his fiancée, so they would have had no way of knowing that Dr. Tobel had written a coded message or where he had hidden it in Miss Eberli's apartment. They could not have informed Professor Moriarty about it, either, or told him where the coded message was, so that he could stealthily retrieve it later while posing as an electrician.
As Holmes and Dr. Tobel approach 221B Baker Street for the first time, Dr. Tobel trips over rubble and Holmes says "You must get used to our London blackouts." But as soon as they enter the flat, Holmes turns on the lights with the window curtains open - a clear breach of blackout procedure. Nor do Dr. Watson or Mrs. Hudson close the curtains or say anything when they enter.
When Sherlock in his Lascar disguise goes on his pub/bar crawl, in the second pub, the Golden Hawk, the dartboard he stands in front of is hung wrongly, with #20 at 1-o-clock instead of 12-o-clock.
Professor Hoffner's first name is shown as being spelled "Frederic" on his door-sign, yet both Holmes and Moriarty verbally spell it out incorrectly as they are deciphering Dr. Tobel's coded message --- Holmes spells it "Freddrick", and Moriarty spells it "Frederick". It is quite unlikely that Tobel --- as scrupulously careful as he was trying to be in every step of his endeavor to keep the Nazis from gaining access to his bombsight --- would have "naively" (i.e., assuming it was spelled the "regular" or "American" way) spelled Hoffner's first name incorrectly, especially in such a vitally-important message.
In the final scene, Charlotte Eberli had since gotten married to Doctor Tobel, so Inspector Lestrade would have addressed her as "Ma'am", not "Miss".