River Song tries to grab a gun and grabs a banana instead with her left hand, but when she aims it at The Doctor, she holds it in right hand.
Hitler is shown using a revolver. While there were a few revolver models in use in Germany at the time (most notably the Erma ER77 - a replica of the Smith & Wesson M19), Adolf Hitler is only known to have regularly carried a Walther PPK (which he used to kill himself), and more rarely a Walther PP.
The Judas tree is not poisonous, in fact the flowers are edible.
Hitler is shown residing in the Neue Reichskanzlei (New Imperial Chancellery) - however, in 1938, construction of this building was not yet so far advanced as that any of the state rooms were finished. Plus, the view outside the window shown (with the Brandenburg Gate on the right-hand side) would not have matched the view from either the Old or the New Imperial Chancellery.
At one point River Song confronts a group of German soldiers three of whom are armed with MP 40 sub-machine guns. This scene takes place in 1938 and while the gun was designed in 1938 it was not produced until 1940.
The correct gun for this period would have been the Bergmann MP-35 although it was produced in relatively small numbers.
In the flashback to Amy, Rory, and Mels' growing up together, there is a scene where Amy is waiting as Mels is released from jail, then the three are seen in Amy's bedroom discussing why Mels stole a bus and drove it through a park. The outfit Amy is wearing at the jail is the same outfit she is wearing in the field and later in 1938 Germany (note the orange leggings). The outfit is similar during the bedroom conversation but the leggings are missing.
When Mels pulls her gun on The Doctor, we hear the hammer being cocked, but Mels' thumb doesn't touch the hammer.
When Rory steps hard on the brakes of his Mini in the wheat field, the tires squeal. That is not possible on a dirt surface.
If a time traveler wishes to kill Adolf Hitler, they would find the job very difficult if they went to 1938, by which Hitler was already the leader of Germany and had already put in motion plans to start World War II. It would be much easier to travel to some time between after April 1889 and around 1900. If the idea of murdering a small child (Even if that child is Adolf Hitler) you could always go to some time shortly before 28 September 1918 and tell Henry Tandey that sparing the wounded German solder he will meet in Marcoing, France would be a bad idea. That way you don't even need to get blood on your hands. Let Tandey do it, as he should have done.