I find the idea of the world being forgiven of their sins by the death and torture of a man to be a something that is very twisted. In my opinion, everyone should be responsible for their own actions and it simply doesn't make sense to punish one man thousands of years ago for someone else's crimes. And it especially doesn't sound right for an all knowing, all loving, and all powerful god to come up with such a horrible solution to a very serious problem either. To be honest, I wouldn't put much stock in the bible as I don't think it accurately relates to reality. Thus, I highly doubt that a "judgment day" will ever happen as much as I doubted the 2012 apocalypse or any other end of the world claim. Claims, in my opinion, should only be taken seriously if there is sufficient evidence and reason to believe them. Otherwise the claim is completely unsupported and should be discarded as such.
As for what you said specifically about judgment day I don't think it is entirely correct to say that people would be judged according to how they lived their lives. People would certainly like to believe that but it is my understanding that living a good life and doing good deeds is not as important as whether or not you believed and worshiped the correct god. I keep thinking back to Dante's Inferno where the first circle of hell is reserved for those who actually did live virtuous and good lives but were simply born in the wrong century, country, family or weren't baptized. It's not just that but many other branches of Christianity would probably claim the same thing, if you aren't a believer or one of them--regardless of your actions--you go to hell.
While I'm curious about where in Pauls letters you found this, FYI Paul wasn't a prophet, nor disagreed with anything Jesus stated. As Jesus prophesied the end of the world, and gave His people a list of signs to look for its coming, I'd say Judgement Day is a sure thing.
Well Jesus, aka the main source of Christian authority, said that the eschaton would come within the lifetime of at least some of his disciples (Luke 9:27), so it's fair to say that the Bible got some stuff wrong. There's New Testament was written over a very long period of time, in both Jewish, Gentile and Hellenistic contexts. Ideas about the end of the world changed throughout the time that it was being written, edited and formed into a canon, so there's bound to be a lot of contradiction. If you planning on taking the Bible word for word, you'll have problems.