Factual error: When the so called "Immortal Beloved" visits Beethoven's grave at the end of the film, it is an 8 foot obelisk, but the original grave was about 2 feet tall, and on the other side of Vienna, in a different cemetery. Beethoven was exhumed in the 1880's and moved to his current location with the 8 foot obelisk, along with Schubert. The woman is visiting a grave which was built 30 years after she died.
Factual error: If you look closely at the stage during the premiere of the 9th symphony, you can see there are no timpani, no brass, very few woodwind, and around 20 strings. Not only would it be impossible to perform the 9th with no timpani and brass, but it is well documented that the contingent of strings at that premiere was at least 56, triple the normal number used and the number shown.
Factual error: After the Countess escorts Beethoven from the stage after Piano Concerto No.5, she says something like, "That is how the world heard of Beethoven's deafness." First of all this was still fairly early in his hearing loss (around 1806), and the effect wasn't as severe as shown in the film. Secondly, he was actually very public with his hearing problems when they did arise (he gave his last piano performance in 1814), often shouting in conversations and using ear horns.
Factual error: Throughout nearly all of the movie the adult Beethoven is nearly or completely deaf. In fact, he only began to slowly lose his hearing in his early 30's, and was able to mostly hear normal conversation until his mid 40's. He wasn't completely deaf until the age of 50. His hearing loss was a very gradual one, and he performed in front of audiences well into his 40's.