I think the correct answer is: it depends. "I think everything will be OK. I don't think there will be any problems" : you are referring to a future situation and making an assumption according to that. "I think everything will be OK. I don't think there are any problems": you are referring to a future situation based on current facts. However I do agree this sounds at least awkward and/or incomplete so you would rather say "I think everything will be OK. I don't think there any problems anymore".

In this context, it's better to use the future because you used the futur in the sentence before.

If u are referring to the problems in future, you'd better use "I don't think there will be any problems." (^^)