Let's tackle this one step at a time, shall we? Standard disclaimers apply, YMMV, IANAG (I am not a Geneticist).
The Nature of Clones - Even though you are a clone, you are technically not identical. Differences arise from a number of issues which impact the way the embryo/fetus/child grows. First we have just plain chance -- Over a lifetime, you genes mutate on their own, and the chances of two peoples' genes mutating in exactly the same way are astronomical. Second would be environmental modifiers. Even if you are a clone of a a previous entity, if you were spawned X decades after they were, you were are subject to different environmental factors at impact your development. This can be as simple as elevation or pollution, or as 'out there' as cosmic radiation and planetary alignment.
Nature versus Nurture - Here, the crux is on whether you believe that personality and mentality are governed by the biological or the sociological. If you feel that biology control it, then the previous argument comes into play. If you believe it's the way they are raised, then the problem in solved.
We already have clones - On average in the United States, 10 clones are Born every day -- they are called twins. They are as genetically similar as you can get, and yet they are always considered individuals. They tends to develop their own personalities as time goes on.
Now, I haven't even delved into the argument of 'Do clones have souls?' because that really deserves it's own node.. written by someone else, preferably.
Someone questioned me on the issue of genes mutating. Let me clarify: By mutate, I mean single-combanant changes. not growing wings. It's documented well that this happens, but usually doesn't have any great effect, except in the case of things like cancer; plus, the number of genetic mutations that are retined in the body are quite low, probably in the low hundreds (which is a very small number considering the total number of pairs in a genetic strand), and usually occur in so-called 'attribute' pairs which govern things like colour instead of those that govern vital fuction. It's simply splitting hairs.