Many excellent books have been written on Biblical criticism, for example, 'Who wrote the Bible?' by Richard Elliot Friedman (buy it here), and it is a subject widely taught in universities. 

(Click here for a list of logical fallacies and inaccuracies in the first 88 pages of Friedman's book)

It turns out that basically all Bible criticism is based on one of three things; archaeological evidence, linguistics, and science.

This is a much longer discussion, but in brief:

a) Archaeological evidence:

Archaeology is by nature fragmentary, incomplete, and open to interpretation. We're not really sure what anything we find is, especially not in context, and we also don't know what we'll find next to fill in the gaps. 

(Added to this, apart from the Sinai event, the Torah doesn't actually need to be historically factual (although I believe it is). It's not meant to be a history book — just the Divine Being communicating the Truth to us, possibly through stories, metaphors, and analogies). 

b) Literary, linguistic factors:

The leading theory in this field, the Documentary Hypothesis, proposes that the Torah was derived from originally independent, parallel, and complete narratives, which were subsequently combined into the current form by a series of redactors.

The literary and linguistic factors, for example, repetitions, different styles, genres, and anachronisms certainly make it clear that the Torah wasn't written by one person at one point in history. That leaves two options: several people over many years or one Divine Being who isn't restricted by and doesn't need to conform to human literary norms. See here for a more thorough refutation of this hypothesis. 

c) Science: 

The science vs. religion debate continues unabated, with no decisive proof either way. For those of you interested in learning about the opinions that say Torah and science are not in conflict at all, and even how science is now coming to bring evidence for the Torah view of life, you can check out the work of Dr. Gerard Schroeder — a Ph.D. physician from MIT (buy one of his many books, Genesis and the Big Bang here). For a different approach see the work of Rabbi Nathan Slivkin (buy his book The Challenge of Creation here).

Needless to say, these works have their critics; as I said, the debate continues. Having done a lot of research on the matter, I have come to the conclusion that there is no way the intricate make-up of the world and all the organisms therein could be random. Others disagree. Suffice it to say there is enough evidence either way to support your particular cognitive bias.