All your sentences seem grammatically correct to me. However, I wouldn’t say ‘plenty of the film was worth watching’. It sounds a bit awkward somehow. I prefer ‘a great part of the film’. But this is only my personal opinion and preference.
As you know "a lot of"and “plenty of” are used both with countable and uncountable nouns.But there is a tendency to use "plenty of "mainly with uncountable nouns. It’s often used in informal speech also.
I agree. Using “plenty of” sounds awkward. This is especially true when the phrase is used at the beginning of the sentence. I think it will sound better if it is used at the end of the sentence.
Yes, mrdmrd, it is correct to use the article ‘the’ with these phrases whenever you refer to a specific noun or in place of the demonstratives (this, that, these, those).