That's a good point. We saw sporting events being watched in the bar in Episode II, so there ought to be news broadcasts and even a "C-Span" for the Senate.
Considering the number of attempts on Padme's life, a lot of questions would be raised over her death.
Anakin might have been famous before he left Tatooine if a certain pod race was broadcast off world.
It would have been interesting to see the propaganda broadcast by both sides in the Clone Wars.
I've often wondered how the Empire tried to make the Rebellion look bad in the eyes of Joe Average Imperial citizen.