When Mary goes to convince Jack Ross to give up Rose he offers her some tea and says "can I get you a cup" when he says cup he his real British accent comes out.
At approximately the 28:00 mark, in a scene where the Dowager Countess interrogates Aunt Rosamund and Lady Edith about their plans to travel to Switzerland for four months, the statue of Mercury keeps appearing and disappearing over the Countess' right shoulder.
When Tom spots Rose and the band leader having lunch, the windows on the outside of the cafe are clear glass with 5" by 12" panes. He goes inside the cafe and the windows are different. They are now 12" by 12" and have opaque frosted glass, no way he could have seen through them from the street. There is a camera shot from behind Rose where we see Tom standing in front of yet another set of windows, these are regular size and are nothing like the others we saw. This scene was obviously shot in three different locations.
At about 3:15 Rose is talking to Jack Ross on the Downton telephone, and hastily hangs up as Cora appears. But as soon as Cora walks away, Rose picks the phone back up, taking the earpiece off the table rather than where she left it hung on the main piece, as if she had only set it down rather than hung up.
Daisy goes off to visit her Father in Law on the farm. They drive a tractor up into a field for a picnic. The tractor is parked close by and behind Daisy when they spread the blanket. A few scenes pass and they come back two Daisy and her FIL on the blanket. The camera changes angles a few time but the tractor is now missing from all shots. This is right around the 53 minute mark for their arrival and 54 minutes for the missing tractor.
At the 47:00 mark as Edith is lifting a basket of linens, it seems that actress Samantha Bond [Aunt Rosamund] says to Laura Carmichael, "Rose, should you be doing this?"
In the kitchen scene where it's discussed about Alfred returning because his father has died, on the table there are eggs laid out. You can see the eggs have modern day 'best before' dates stamped on them.