When Michael and Katie escape from the the bully in the field, Michael's neck-scarf has fallen down his shirt and is no longer visible. After Katie mentions that she didn't care if Michael got hurt, his scarf suddenly is tied prominently around his neck and plumped under his chin.
When Darby is in the leprechaun cave and King Brian opens the side of the mountain so that the leprechauns can ride their horses outside a number of rocks fall into the opening. One very large rock lands in the middle of the path. A split second later, when the leprechauns ride out, the rock is no longer there.
When Darby pours the poteen for King Brian, there is a steady stream coming from the jug when the camera is on Brian. When the camera switches to Darby a moment later, the stream from the jug is larger and less steady.
When Darby pretends to take a drink from the mug and pours the liquor back into the jug, he spills much of it, leaving a large stain around the jug neck. When the jug is next seen, less than a minute later, the neck is completely dry.
The goof item below may give away important plot points.
Darby is able to capture King Brian in the stable because, as he explains, a leprechaun can not use their magic in the daytime. Near the end of the film, it is daylight when Katie throws the knapsack on the floor of the pub and Brian turns himself into a rabbit to escape.