In the scene where Emma Thomson is worried about Kate Winslet when she disappears in the storm, she is handed a cup of tea and she looks out the window. In the next shot, someone is handing her the same cup of tea that she had been given just a few seconds earlier.
I noticed that too, but here's what I think happened. Mr. Palmer handed the cup of tea to Ms. Dashwood. Perhaps they shortened the scene (as in Ms. Dashwood having waited for 15 minutes or so). And then Mrs. Palmer refills the cup of tea and passes it to her.
Junie is right, the second handing of the tea-cup is supposed to indicate the passing of time as they are waiting for the Colonel to bring Marie-Ann back.
It's referring to the passing of time, definitly. If you were paying attention...Col. Brandon just walked 10 miles, five there, five back. Carrying her half way. It takes a while.