Which one is the recommended way to form sentences? Or all of them?
a) I was at the movies yesterday watching the newest Indiana Jones. Yes.
b) I was at the movies yesterday and watching the newest Indiana Jones. No. You can't connect two different usages of was with and. (was where and was doing.) You have to repeat the auxiliary was. b) is like saying "She went away in a Cadillac and a bad mood." 
c) I was watching the newest Indiana Jones at the movies yesterday. Yes.
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But note that a) does not have the verb phrase was watching. It's two separate clauses, the second a participial construction. The verb phrase of a clause cannot be separated by phrases like at the movies yesterday.
-- Where were you yesterday?
-- I was at the movies yesterday.
-- What were you doing there?
-- Watching the newest Indiana Jones.
Thus: I was at the movies yesterday. || (I was) watching the newest Indiana Jones (there).
In c) the emphasis is different:
What were you doing yesterday?
I was watching the newest Indiana Jones at the movies (yesterday).
a) is essentially about where you were. What you were doing is incidental added information. c) is essentially about what you were doing. Where you were is incidental added information.
CJ