When Fiona first meets her grandfather the ticket pinned to her jacket is in good condition. The next scene, right before her grandfather lifts her over the fence, the ticket has a large crease through the middle and is crumpled on the bottom.
During the storm on Roan Inish, there is a shot of the rocks holding down the roof moving quite a bit from the force of the wind. However, the rocks in the background of the cottage next door are absolutely still suggesting that the storm is completely man-made and the crew only had the wind machines on the one cottage.
When Fiona is painting the windowsill in the cabin on Roan Inish, you can clearly see that the paintbrush is dry.
Near the end of the film, when the seals push the cradle-boat back into the sea, you can clearly see a hand at the top left corner of the frame grab the cradle and pull it.