First, even though it is a super funny comedy or a horror which make you wideawake in the middle of the night, people try not to laugh or scream. Everyone enjoys a movie very quietly. It's strict prohibition talking or a cell phone ringing.
Next, basically it is common that you throw rubbish of drinks and popcorns into a trash bin by yourself after the movie but it's carried without exception in Japan. You hardly see rubbish on the seats or on the floor. Also I reraly have seen people with their foot on the seat in front of them while watching movies. So seats are CLEAN!
You might find more small differences, but these are the unspoken rules I would like you to know at least.