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".