Marke's castle is stone built in the "motte and bailey" style with a keep and a drawbridge. These didn't exist in Britain until after the Norman invasion - about five hundred years after this film is supposed to be set. Britons, either Celts or Anglo-Saxons built large earthwork defenses or walled their towns with wooden palisades.
In the scene when the barons are gathered, Marke addresses one group as the group from York. Since this movie is set just after the Roman withdrawal from England, York would have still been known as Eboracum.
It is highly unlikely that Isolde would have worn a wedding ring. The Roman custom vanished and did not come back into vogue until the late Middle Ages. In any case, Marke certainly would not have worn one himself. A woman was her husband's property, and the wedding ring was a literal symbol of that ownership. The custom of men also wearing wedding rings is relatively new.
Throughout the entire movie, the term "English" and "England" are used many times. At this point in history, the Angles (Angle-ish, Angle-Land) were just starting to make their way throughout the land and claiming some territory for themselves. During that time, Tristan, Marke and their families would have been called "Britons" or "British" or they could possibly be referred to as "Cornish" since the Britons of that time would rarely identify themselves as one people but rather many factions, and many individual little countries rather than one united.
The references to "Celts" early in the film. The Roman word Keltae referred to Germanic tribes as often as it did Celtic ones and none of the inhabitants of the island called themselves Celts until Edward Lhuyd published his linguistic studies in 1707. The Celts: Prehistory to Present Day, John Davies, Cassel & Co, 2000 pp. 57.
In one of the scenes, Isolde is seen riding with stirrups. Stirrups were not brought to Europe until 600 AD through the Asiatic Avars. They were not commonly used throughout Western Europe until the 9th century. It would be extremely unlikely that an Irish Princess would have stirrups.
The poetry Isolde keeps quoting was written by John Donne, who was only born in 1572. The lines "My face in thine eye, thine in mine appears, And true plain hearts do in the faces rest; Whatever dies was not mixed equally; If our two loves be one, or, thou and I Love so alike that none do slacken, none can die." are from Donne's 'The Good-Morrow'.
At the party when Melot is trying to talk to Tristan and Marke about his choice for second, Melot says, "You don't seem to know what you've done here," but the motion of his lips doesn't match the words.
In the beginning scenes, when young Tristan is carrying his rabbit in his hands past the market stalls, he gets a sprig of something to make his mum the bracelet, and the rabbit disappears from his hands. We know he kept it as it is seen in the scene immediately after inside the keep roasting over a spit.
When Isolde is trying to talk to Tristan in the market his hair is parted to the side. When she pulls him off to the side, his hair is separated in the middle at his forehead, his having no time to move it that way, as Isolde was holding was holding his hands.
At the end when they show the flashback of when Tristan and Isolde are in Ireland and Isolde is reading her poem, Tristan kisses her and she holds up her hands and she is not wearing her shell bracelet. But earlier in the movie during the same scene she is wearing it.
Addressing a crowd of his men, King Marke mentions that they all must ride off into the forest that night, citing a tradition to ride out on the night of the full moon. The camera then cuts to a shot of a waxing half moon, followed by one of the men riding off on their "full moon" ride.
Every Irish king had lots of Irish rivals. None of them had the sort of unchallenged power that Donnchadh is shown as having. Britain in the 5th century was also very split, part-conquered by Anglo-Saxon settlers but anyone might be fighting anyone else.
When Tristan is escaping in the boat you can see that it is clearly a motorboat. A sailboat would not have the bow up in the air as it travels. Also, a sail of that size would not propel the boat with that speed.