(at around 1h 29 mins) The seed Tommy is planting at the end is from a Liquidambar styraciflua, and should not be green during the heart of winter. Additionally, a L. styraciflua seed of this maturation is most likely immature and will not germinate, regardless of the season.
(at around 42 mins) Tikal is mentioned by the Queen's priest, however, it wasn't discovered until the mid 19th century, and the name Tikal ("place of voices") was applied only in the early 20th century by archaeologists. This scene is a novel-within-the-film written by Izzi Creo, whose research may not be perfect.
(at around 44 mins) There was no 'Kingdom of Spain' in the 16th century. Isabella of Castile created a dynastic union by Ferdinand of Aragon. It did not become a coherent single kingdom till much later.
The second brightest star of Orion constellation, Betelgeuse, is missing in the sky views throughout the film.
(at around 42 mins) The map used by the conquistadors to find the Tree of Life is erroneous. The priest says the three points which form an equilateral triangle on the map are Chichen Itza, Yaxchilan, and Tikal. However in reality, the three Mayan sites form an obtuse triangle, with Chichen Itza being the northern-most and the eastern-most point.
(at around 22 mins) The "Xibalba Nebula" in the movie is the Orion Nebula - which is not gold and does not contain dying stars, unlike in the movie. It is largely pink (from ionized hydrogen gas) and is a stellar nursery where young stars are forming. The first stars to die there will be massive and will not create nebulae first (they will supernova instead).