Factual error: The Sheriff of Nottingham seems to use timekeeping as we do today in the modern age of clocks. However, in the 1100's, when the film takes place, an accurate tell of time was only available during sun-up hours using a sun-dial that needed daily adjustment in order to stay accurate. So sundials would save this mistake, however, the use of torches in the scene as well as an additional source of cool light (the moon) suggests it was nighttime when 10:30 and 10:45 were mentioned. (01:05:30)
Factual error: Robin and Azeem land at the white cliffs and Robin says something like, 'Tonight we will dine with my father'. Those white cliffs are the Seven Sisters in East Sussex, about 200 miles from Nottingham. It would probably take about two weeks to walk it. They also reach Hadrian's Wall in the next scene, which is 200 miles further north than Nottingham.
Factual error: There is no reason why the executioner would have an axe just conveniently lying around on the scaffold to use on Will Scarlet. All the criminals were sentenced to hang, he wasn't expecting to behead anybody. (For those thinking this might just be a contingency - beheading as a punishment was only ever used on members of the nobility. It's not like the executioner or the Sheriff would have prepared this as a back up 'just in case' - public executions didn't work like that).
Factual error: When Marian is embroidering at home, she is singing to herself "Le chant des oiseaux", which Renaissance composer Clement Janequin didn't write until the 16th century.
Factual error: Aside from the earlier mentioned mistake of them apparently walking to Nottingham in less than a day, if Azeem was facing Mecca to pray, they set off in a southerly direction anyway.
Factual error: When Azeem goes to pray he starts by kneeling on the ground and soon afterwards he bows down. The Muslim prayer sequence starts by standing up for quite some time then one bow, up again followed by two kneeling bows then up again. Also, Muslims do not put their palms together for prayer as Azeem does, rather their hands are either at their side or crossed.
Factual error: Think of the '100 billion dollars' scene in Austin Powers 2, where the President laughs because that kind of money doesn't even exist. You now have an idea how ridiculous it is that a twelfth century outlaw stealing tax money and robbing travellers could get anything like '4 million' as the scribe mentions. King Richard's ransom was only something like 100,000.
Factual error: Marian tells her messenger to take a letter to the King, who is in France. Problem is, we were enemies with France at that time. The King wasn't even there, he was on his way home from imprisonment having been captured on his return from the Crusades.
Factual error: This pertains to all Robin Hood movies. Robin's back quiver was an American Indian innovation, unknown in Europe until the Age of Discovery. Medieval archers used belt or shoulder quivers.
Factual error: In the religious service there are some incredible mistakes that are really obvious to a historian whose speciality is medieval church architecture. The scene is filmed in St Bartholemew The Great Church in London, which was founded in 1123 and built during Henry I's reign: thus it would have been standing by the reign of Richard The Lionheart, when the film is set. However, several seventeenth century memorials can be seen on the walls of the church, and even a modern wooden hymn board. Some of the upper windows of the church were added in the fifteenth century: we see these on several occasions. The glass in the windows is obviously modern, and while the interior walls of medieval churches were elaborately painted, the walls and stonework are plain and bare. (Admittedly it might have been rather expensive to install coloured medieval stained glass and paint the interior walls, so perhaps we can let that go.) There is a later scene in St. Bartholemew the Great in which a modern altar, candlesticks and metalwork can be seen.
Answer: The white robes, reference to "the old ways", and pentagram across the map when the Sheriff meets the Barons suggests per-Christian Druidism; the upside down crucifix certainly implies Devil-worship. These two spiritual paths are, by nature, mutually exclusive. In short, a fictional pseudo-witchcraft invented for the film, yes.