Given that much of the works during the Medieval period were narrative prose, the stories were embellished by the scop so as to keep the attention of the courts. Therefore, many of the stories were told in first-person and third-person randomly interchanged.
The scop would add in "I" or "methinks" so as to add to the story in a way which would suggest that they were either there, as a statement of their admittance that they are retelling a story they heard, or to make the story more personal.
The point-of-view in "Sir Gawain and the Green Knight" changes at the end of Part III. In Parts I through II, the text offers a historical view of what was happening prior to the action of the story. In Part III, the actual story begins. It is Christmas time and the knights and guests of King Arthur are gathered at his castle to celebrate.
The end of Part III offers a more intimate view of the people at the Christmas celebration. The scop's story becomes much more specific regarding the actual happenings at the celebration. Here, the point-of-view becomes much more omniscient given the scop details much of the scene from his own "recollection" of the story he was told.