When Mr. Stevens is serving at the banquet, he stands behind Lord Darlington's chair empty-handed. Then he suddenly leaves the room to receive news of his father's death, but at the end of this scene he now has a decanter in his hand, which isn't used until the next scene when the guests have left the banquet, and have been in another room for quite some time.
(or possibly just character error) At the very beginning Miss Kenton mentions a conference "back in 1936". At the very end of the film, Lewis asks, "Isn't this the same room where we all attended that banquet back in 1935?"
We see a dozen bottles of Graham's Port being delivered for the banquet - but the port would have been cellared for at least six months before being decanted - vintage port is undrinkable immediately after being transported; and later Stevens takes (and breaks) a bottle of Dow 1913 vintage port- but no producers declared a vintage in that year. 1912 was a vintage year, and the next one was 1917.
In one kitchen scene, in preparing for the banquet, we see a meat cleaver beheading a pheasant. However, when the head is thrown away, it is obvious that the head was previously severed, as the cleaver rests on a non-severed part of the pheasant's neck.