Annoyed by the spelling mistakes in the article, Maude Flanders took a red pen and began to edit it.
Is it complete or incomplete sentence ?

If "it" is clarified, yes.

Explanation:

beowulf sets out on his journey for daneland. -- 1

hrothgar welcomes beowulf. -- 2

beowulf waits for grendel to attack heorot. -- 3

beowulf succeeds in defeating grendel by tearing off his arm. -- 4

beowulf fights with grendel’s mother. -- 5

beowulf sets out for his fight with the dragon. -- 6

beowulf sets out for his geatish homeland. -- 7

“way of writing” should be replaced with “writing style"

“idea” should be replaced with “purpose.”

maybe   “people from a long time ago” should be replaced with “elizabethans.”