It seems to me that advertising, in some cases, has turned into a modern "protection racket" of sorts.
"Pay me the money... or else!"
"Or else what?"
"Or else we'll tell everybody the wrong showtimes and mess your business up! And at the same time we'll collect from your competition who won't stand up to us and make them look good."
The conversation above is purely fictional, but it seems to capture the content of this thread and also captures the way I feel about many advertising companies, online and off. I'm sure there probably is no company that maliciously publishes incorrect showtimes or performs any act against those who don't pay to advertise. But, by being negligent when they advertise a theater's information (as an unsolicited service) and get it wrong with no concern for the results, that is nearly as bad. They carelessly sell false information to their customer's, such as Google Movies or whoever. Sure, mistakes are probably inevitable, but if they don't correct their mistakes when asked, it seems to me that would be an actionable offense. So, if they publish the wrong information, ask them to correct it. If they refuse, then maybe you should seek legal counsel. If they don't want to provide a free service, I don't think there is anything you can do about it, unless you can prove discrimination or antitrust violation, or some other type of conspiracy against your theater.
Since I'm not a lawyer, my advice is probably worth what you paid for it.
When I was operating my theater, I didn't even pay for a yellow pages ad. I was the only theater in the county and everyone knew it. In this kind of situation, your customers will find your information wherever it may be. You do your best to put it in convenient locations, and that is all you can do. You don't have to hurt yourself in the process by overpaying.
I remember Verizon Super Pages called me and tried to sell me an online listing. He wanted a lot of money, just like cinema source. I gave him a quick "NO".
There are so many phone books that come out each year. Every one of them is from a different company who likely makes the merchant feel like he should advertise in all of them to avoid missing out on customers who find the competition's listings.
You just can't advertise everywhere. Some bigger companies will, but not everyone can justify it. Only spend money where it brings you customers. Forget the rest who are in the "protection racket".
If your information isn't on Google or Yahoo or is incorrect, then maybe you can put up a sign in the Lobby or create an on-screen announcement that says, "Find our showtimes on (insert your site or preferred info providers here). Other sites are not authorized to provide our information and may do so incorrectly."