When people are being evacuated from Theseus' village, one of the carts used has modern (post-1900) bicycle wheels, complete with metal spokes (painted black) laced in a cross 3 pattern and chrome plated double flanged hubs. These would not be seen until the start of the 20th century.
The Thief says his name is Stavros. This translates as Cross and is one of the most common Christian names in Greece, referring to the death of Jesus. But it is very out of place in a story set long before Christianity was established.
Before the "Henry V speech," Theseus vigorously climbs up a rusty metal ladder to a higher part of the defense wall. The metal ladder is made from welded steel construction pipes (HSS or hollow structural section). Structural steels was first used in the 1700's and the process of welding used was first discovered in 1802 AD. That's just a bit too late for the "Renaissance painting" design of the movie. (See also the "incorrectly regarded as goofs" item about the Titans' cage.)
King Hyperion's men are incorrectly referred to as "Heraklions". The city of Heraklion was founded in AD 824, 2,000 years after the movie setting. Hyperion (analogous to the classical King Minos) and his men should instead be called "Minoans", which was the culture of the time for Crete, where they are suggested to come from. Similarly, the "Hellenics" should be referred to as "Helladics", for the same reasons; "Hellenic" refers to a much later period of Greek history (323-146 BC).
On the morning of the battle, when Hyperion walks to the front of his army set to attack, all his soldiers are wielding their weapons in their left hand, shields on their right. When the shot switches to the front, all the soldiers have their weapons in their right hand.
Although the opening text places the movie in 1228 BC, there are numerous examples of weaponry, fashion, architecture, plumbing, design, etc., from much later time periods. It should be remembered that this movie is about fantasy, not history, so there is no attempt to recreate a specific time period accurately. The filmmakers stated that they based the look of the film on Renaissance painting styles. As long as the technologies and designs in the movie are something that existed by the 16th century, and therefore artists of that time could have conceived of it, they get a free pass and are not regarded as goofs.
The Titans are biting pieces of PC-52 steel reinforcing bars (first used around 1700 AD). However, this is the prison constructed by the Gods to imprison the Titans. As a magical construct, it doesn't necessarily conform to any real world materials or follow real world physics. (There are other examples of re-bar used throughout the film which can't use this excuse, as they are not godly constructs.)
During the "Henry V speech", the soldiers repeatedly bang their shields in agreement. Several of the soldiers are a little too enthusiastic and it can be clearly seen that the silver spray paint covering their shields is tearing off. One soldier (middle-left) has almost completely stripped the top-left section of his plastic "shield."
When Theseus takes his mother's body into the temple he cuts his right leg and walks in bare feet, but moments later when he's fighting the beast with the barbed wire helmet he has gladiator-style sandals on. He has no shoes on, on the way in deliberately to leave a trail, although not shown one can infer he had shoes with him as well by the way he followed his foot-trails on the way out as he never ventured into the maze with his mother to honor the gods prior to her death, thus would not have known the way out. Furthermore, this is probably a sly allusion to the method (a ball of string) that Theseus used to escape from the labyrinth according to ancient mythology.
The Epirus Bow is clearly a modern day Olympic style "recurve" bow. It's a left-handed bow, Theseus is right-handed. For him it would be next to impossible to hit a target shooting a left-handed bow. But there is a supernatural element at play here, so real world physics need not be strictly adhered to.