When Vlad meets with Mehmed in his camp at the beginning of the film, he mentioned the Turk's fine coffee. However coffee would not be known in Europe for approximately 50 more years, when Columbus brought it back from the New World.
Vlad never ruled in Transylvania. He ruled in the neighboring country, Valahia. The Cozia Monastery is in Valahia, it did exist in Vlad's lifetime, but is was not fortified and not likely to be use during wars, as the place does not have a real military value. Most likely during wars Vlad would retreat to Poenari fortress, a place not mentioned in the film, but much closer to Vlad's capital than Cozia Monastery.
The second time Vlad enters the cave, a tarantula can be seen. While creepy, that particular spider is a golden knee tarantula, native of the Chaco region in Argentina, South America. The action takes places in Eastern Europe.
Various characters speak in Turkish during the movie, however the Turkish they speak is both heavily accented and often grammatically incorrect, making it obvious that they're not dubbed by native Turkish speakers.
Vlad III was not known as Vlad the Impaler during his life, but was rather given the nickname posthumously. Therefore, he would never have been called this by anybody, as he is several times in this movie.
The external walls of the Cozia Monastery are covered in fresco paintings. Cozia Monastery does not have such external walls, however the churches from the neighboring country (which in Vlad's time would be Moldavia) do have external walls covered in fresco paintings.
While in history Mehmed first defeated Vlad (Vlad Tepes) in 1462 and Vlad fled to Hungary and prisioned until he released in 1474.
In 1476 he attacked to Ottomans and defeated again but this time Vlad's head was brought to Mehmed as a proof. Mehmed died 5 years after he defeated Vlad III for the second time. After he defeated Vlad III he put Radu in that position and the region was still a part of the Ottoman Empire till 19. Century.
This is a fictional movie that is based on the fictional writing Bram Stoker.
Vlad jumps after Mirena in an attempt to save her when she's falling off the tower. And though he can move faster than lightning, and should be easy for Vlad to overtake Mirena while falling, he never catches up to her. However, it is made clear that the sun is rising, which would weaken his power which is why he can not catch up.