Many new forms of entertainment were unveiled, such as jazz music, salsa dancing, and silent films.
Should such as be accompanied with a colon? Should there be a comma after unveiled?
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The sentence is coherent and syntactically correct as written. But if you're worried that it seems run on, you might want to phrase it a bit more tightly.
You can tighten the sentence in either of two simple ways. One is to bring the examples closer to the thing that they are examples of (namely "forms of entertainment"), while leaving the rest of the sentence unaltered:
Many new forms of entertainment—such as jazz music, salsa dancing, and silent films—were unveiled.
The other is to bring the examples and the "forms of entertainment" closer together by making the sentence active rather than passive (which entails identifying the person, people, or entity responsible for the unveiling of the new forms of entertainment):
The Pilgrims unveiled many new forms of entertainment, such as jazz music, salsa dancing, and silent films.
The sentence is grammatical as written.
When you use such as a colon is not necessary. The colon would be better used if you constructed the sentence without it:
Many new forms of entertainment were unveiled: jazz music, salsa dance, and silent films, to name a few.
I would say that comma is optional. It neither adds to nor detracts from the sentence.