The first one that I'd like to address (one that I saw today), is the idea that God always exercises his will/plan over our lives.
I believe the Bible makes it clear that God does not exercise control over everything that goes on in this life. The primary thing that comes to mind is found in what we call "the Lord's prayer." This is a passage found in Matthew 6 where Jesus is teaching his disciples to pray. Here Jesus says, "Your will be done on earth as it is in heaven." From this verse I think 2 things are clear: God's will is not always done on earth, but it is in heaven.
Also, another verse that comes to mind along these lines is 2 Peter 3:9 where Peter writes that God is, "not wishing for anyone to perish, but all to come to repentance." But as the Bible indicates, not everyone will come to repent and follow Jesus. Clearly, this is an instance where God wants something to happen that doesn't always happen.
And another, Old Testament, example is found in Job where God gives Satan permission to effect some of the people and things around Job, but limits what happens. I think this is the best example as it is clear that God is allowing, but not directing the events. Satan is a created being and the ideas/concepts behind his creation and his ultimate role in our lives and God's plans is very difficult, if not impossible to grasp...but that is another topic really.
I think the confusion/difficulty comes in the concepts of God's timelessness, omniscience (all-knowing) and the fact that He created the whole thing. So while there are problems, they are problems with what He created and that He knew would happen when He created it. I believe this truth is also something greater and beyond all of this life that goes beyond our 80 or so years alive in this world. But, in conclusion, to say that everything that happens to us is "part of God's plan" is incorrect on a basic level.