Why did Moshe need to see the Eigel? Had Hashem not already told him about it?
Oznayim la'Torah #1: Hearing is not comparable to seeing, which makes a more powerful impression on a person. Consequently Moshe's anger was amplified when he ctually saw the people worshipping the golden calf and he decided to break the Luchos.
Oznayim la'Torah #2: When Moshe saw that it was not just a matter of bowing down to an idol but dancing with joy - and simultaneously commiting adultery and murder, he realized that they would not do Teshuvah, even when they saw the miracles that surrounded the two Luchos, 1 which would not stop them from the path that they had taken - and that they therefore needed to be broken.
Oznayim la'Torah #3: Moshe actually brought down the Luchos with the expresss intention of breaking them before the eyes of the people. 2
The Halachah prohibits believing Lashon ha?Ra, irrespective of who says it. Consequently Mohe did not believe that they irael were sorshipping the Eigel till he saw it.
What did Moshe see?
Da'as Zekenim and Rosh: He saw that the letters [of the Aseres ha'Dibros] flew off the Luchos. Therefore, he grabbed them and broke them in front of Yisrael's eyes.
Oznayim la'Torah: He saw the second thing that Hashem referred to when he stood before Him by the burning bush. 1
Refer also to 9:16:1:1 &2.
