i did post a link where they discuss the arguements within biology between the so called gradualists and punctuated equilibrium-ists (or as they called each other, the creeps and the jerks) It is interesting to note that jerks seem to occur in fossil records (which only record dense bone material, and thus miss a lot of other changes are going on) while the gradual-type changes were predicted by, what, an understanding of DNA, and perhaps point like errors - this two ideas seem to contradict each other. But in both cases we're not really getting a full picture, we're talking about specialities who separately study parts of a whole and need to work out the details (which perhaps the current generation of scientists have done, i'm not sure how old the gould-type vs darwin/dawkins-type arguement spans from, though again i'm not a historian of science, so i've relatively little interest in that topic)
I think i also pointed out that we're only now learning that the simple one gene for one protein idea of DNA has been demolished by new information. The last decade has lead to the emergence of an understanding of how networks of gene work in concert, and a series of changes can occur in a species from one changed gene (if that gene turns on and off several other genes)
As to your question. Look at Down Syndrome, that is a fairly common genetic error which results in an extra chromosome, no new genes are added, and thus no new 'information' but double the genes (on that chromosome) mean twice the proteins produced (or in a non-linear system, not exactly twice, it could be f(x)-> 2x^2 + x + 1; which would mean 2x chromosomes gives us 2(2x)^2 + (2x) + 1 proteins...) And the resulting changes in the human are massive. Far more than any gradualist theory of a single cell - which you seem to be worried about.
Ok i'm not talking about height here, and i'm not even talking about a small mutation. Further i don't even know if Down Syndrome suffers are fertile (though i suspect either 50% or 100% are) BUT some gene copying errors - and fairly simple ones - can have a huge impact on an individual.
It think you are failing to see the complexity of the system you're talking about. And are simplifying it a bit. A human doesn't need any genetic mutations to end up with a very long neck, or big holes in their ears, extra cells are produced to cope with environmental changes, such as slowly sticking ever larger things into your ear or lip, or the Karen Hill tribe: http://albertandrhonda.blogspot.ie/2011/02/karen-long-neck-tribe-human-zoo.html
It is when you take into account the non-linear effect of genetic networks (that is a network of genes which switches on and off other functions within a cell, which is part of the way different cells in your body had all the same genes but each acts differently and has a different function) the variety of mutations from duplication errors, copying errors, insertion errors, deletion errors, etc. You could get your 2x^2 + x + 1 worth of proteins being changed to 2x^2 - x +1 which still gives a similar amount of that protein for lots of x. (by the way i'm making up numbers here) But if you have a network where one gene is responcible for the 2x^2, one gene for the sign of the x and a separate mechanism for the +1 (it occurs in all cells regardless of x, lets say) - and by the way, x may be the level of some other chemical/protein in the cell/environment, so could vary across the body and result in different cells doing different things. Oh My.
Your simplified explanation/understanding lacks soo much of the complexity (much of which i don't understand, and some of which nobody understands) that you're getting stuck on somewhere... If you want to go further, i suggest a biology degree, and then a genetics masters.