At the beginning of the film, during Mr. Stevens voiceover, he recalls the day Miss Kenton arrived. It was, he says, the day of the Charlgrove Meet, which is a fox hunt. We see the hunt riding through the estate, the trees of which are covered in green leaves, making it summertime. Yet a hunt usually takes place in winter and in the next scene, Miss Kenton is being interviewed in Stevens office, the same day, but the calendar on the table reads Wednesday, 25th October.
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?"
Early in the film, the now elderly Stevens sets down a rack of toast on the breakfast table for Congressman Lewis, who is now the master of the house. Lewis is seen reading the paper and talking with Stevens. He doesn't take a slice of toast from the rack. The camera cuts to Stevens, who is bringing a cup of tea to the table. When he arrives at the table, Lewis is halfway into eating a now buttered slice of toast.
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.
After Richard Carlisle drops off Stevens and empties the can of petrol into the gas tank of the car, the Daimler starts up right away on the first try. Considering that the car stalled because of fuel starvation due to an empty tank, the engine would be unable to start until the fuel pump has operated long enough to pump the gas from the tank to the float bowls of the carburetor. It would start eventually, but not instantaneously.
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.