In the first scene, the Professor can't read the note he is given by his assistant, but he had been reading and writing in his notebook without glasses before that.
In the chase scene by the cabin in the mountains near the border, it can be seen clearly that there is some kind of cable attached to the officer's left foot.
At the reception in the English embassy, Professor Smith misquotes Lewis Carroll's Jabberwocky. He mispronounces "borogoves" in the third line of the poem as "borogroves".
Although Professor Smith's first name is Horatio, in several scenes he is called Horace by his brother and others.
Horace would be correct for someone called Horatio, that most famous one called Nelson, was as a child called Horace; this is well documented.