First, let me apologize for having not read all of the comments, although I did read through a lot of them. But I would like to write a few things (my take on it, if you will).
First, the word 'truth' does not have the same meaning in all contexts. In the most general sense, the 'truth' might connote the way the world is -- irrespective of what anyone might believe about the world. That is the most general sense, but (other than perhaps stating that one does believe there is 'a way the world is') it's fairly vacuous, as there is no 'way the world is not', independent of our beliefs. In that sense of truth, the problem is less about the world being some way, and more about the issue of how we can know the way the world 'really' is.
But to get to a more specific notion of truth, 'truth' can be a property of declarative statements (whether exclusively or not, is debatable...for example, whether a 'theory' is really a good candidate for 'truth). In the realm of statements, what it means for an empirical statement to be true, for example, is different from what it means for a mathematical statement to be true, or an ethical statement or an aesthetic statement (if they can in fact be true). These are very hotly debated topics in philosophy.
Given that this is a physics forum, let's take a basic 'observation reporting' claim for an example:
'That (object) is red'
Now, according to the traditional correspondence theory of truth, that statement is true if in fact the object is red. But, we are immediately vexed with the issue that there might not be 'red' objects in the world independent of observers -- which means that the statement, said all in good faith and in the presence of what appears to be a red object, does not accord with our notion that truth is the way the world really is, independent of our beliefs -- furthermore, if there is no red out in the world independent of observation, then there is literally nothing for the term 'red' to correspond to. This simple notion of correspondence is much too flimsy.
A preferred model, one that I am currently thinking a good bit about, is that what makes these kinds of statements true (statements actually uttered in the seeming presence of objects that the statements are about) is not that necessarily they (although sometimes they might) correspond to some 'thing' out in the world, but that the very meaning of the statement is a product of being in a particular sensory state (having a certain kind of experience...in this case having the experience of red). So, what the term 'red' means, just is having a certain kind of experience. Statements using that term are true when those statements are uttered while undergoing a particular experience.
In terms of corresponding to a world, the following is about as far as I would go. When one makes a statement like 'That (object) is red', something is going on in the world...a 'state of affairs', such that when one is having an experience of red, one is also a component of a particular state of affairs of which some aspects are directly relevant to actualizing the having of such an experience -- when one utters the statement while being a component in this state of affairs (which surely not only includes whatever is going on 'out there' but one's eyes and brain and everything else), then one's statement is true...and we can say that it 'corresponds' to the world.
That is a model, and a plausible one I think, for what it means for very basic observation type statements to be true. But it is also an oversimplified model. It doesn't take into account that even the most basic observation statement presupposes a complex conceptual apparatus available to the speaker...much of that conceptual apparatus not derived from the immediate observation being reported upon...