The adjectives errant and arrant have been mixed up for centuries, but modern usage prefers to keep them apart.
errant: itinerant, traveling
This is the sense present in the term knight errant. The knight roams around looking for maidens to rescue, dragons to slay.
Errant is often used to refer to something that has gone astray.
Woman struck by errant fire hose dies
The Cheonan sinking: The errant mine theory
South Berwick Rod & Gun Club closed after errant bullet found
The word errant can denote error in opinion or conduct.
Phuket Police Chief: ‘I Will Pursue Errant Officers’ (i.e., officers suspected of misconduct)
Errant gene may make some people age faster
[taking scripture out of context] will inevitably lead to errant teachings and inaccurate assumptions about God’s word.
It is only the errant translations and errant teachings of the church that cloud this fact.
arrant: notorious, manifest, downright, thoroughgoing, unmitigated
One speaks of an arrant fool, an arrant liar, an arrant hypocrite, etc.
The word arrant occurs 16 times in the plays of Shakespeare, most frequently in the speech of the “low” characters.
Falstaff: An the Prince and Poins be not two arrant cowards, there’s no equity stirring –Henry IV, Part One, II, ii
Dame Quickly:Yonder he comes; and that arrant malmsey-nose knave, with him. –Henry IV, Part Two II,i
Robert Shallow: Use his men well, Davy; for [they]are arrant knaves and will backbite. –Henry IV Part Two, V,i
Dame Quickly: No, thou arrant knave; I would to God that I might die, that I might have thee hang’d. –Henry IV, Part Two V,iv
Gower: Why, this is an arrant counterfeit rascal; I remember him now; a bawd, a cutpurse. –Henry V III,vi
The blustering Welshman Fluellen in Henry V is especially fond of the word:
Kill the poys and the luggage! ’tis expressly against the law of arms: ’tis as arrant a piece of knavery, mark you now, as can be offer’t; (IV,vii)
his reputation is as arrant a villain and a Jacksauce, as ever his black shoe trod upon God’s ground (IV,vii)
‘Sblood! an arrant traitor as any is in the universal world, or in France, or in England! Henry V (IV,viii)
Your majesty hear now, saving your majesty’s manhood, what an arrant, rascally, beggarly, lousy knave it is: (IV,viii)
The word arrant remains in use, as can be seen in these examples from the web:
either [he] is a horrible person, a wretched ghoul…or he is an arrant liar under oath,…
The man’s an arrant womanizer…
Their deaths are a tragic commentary on the arrant cowardice of “freedom fighters” and the inept leadership of those utterly undisciplined terrorists.
The man opposite shook his head, catching sight of her at the exact same moment that he did so, arrant disbelief in his eyes.
Bottom line: Use errant if you mean wandering, straying, or erroneous. Use arrant if you mean downright, complete, or notorious.