Open questions
One question, and what would settle it.
When was Beowulf composed, as distinct from when the surviving manuscript was written?
Why it is open. The one manuscript is dated on palaeographic grounds to about 975 to 1025, and that date is not seriously contested. The date of composition is, and estimates have ranged across three centuries. Arguments from metre, from linguistic archaism, from the historical allusions and from the poem's Christian frame have each been made to carry the case and each has been answered. The atlas records the manuscript date as a date and the composition date as disputed, rather than choosing.
What would resolve it. A dating argument that does not depend on assumptions about the transmission it is trying to establish. Linguistic and metrical tests have been the most productive line, and a test whose result is independent of whether the poem was copied and modernised on its way to the surviving manuscript would settle far more than another reading of the historical allusions.
Field. Old English philology, historical linguistics and metrics, palaeography