Shamir Scheme: Whats the problem of not using random x-coordinates?
i would like to know why there is a problem of not using random x-coordinates in shamir secret sharing schemes.


There is no such problem.

The only requirements on the $x$-coordinates are:


They're all in the range $(1, p-1)$ (or $p^k - 1$ if you're using the extension field $GF(p^k)$; you can't use 0 as a coordinate (as $f(0)$ is the secret), and you can't you values outside the range.
They're distinct (if they're not, then the two shares with the same $x$ coordinate are the same share).


ANy arbitrary set of $x$-coordinates that meet these two requirements work just fine.


  So, why i always find in some literature that it is a problem using not random x coordinates?


I suspect that you are misinterpreting the literature.  For the coefficients of the secret polynomial $f(x)$, it is necessary that the non-constant terms be random; if they are not, then it is possible for a small group to recover the secret.

There is no corresponding requirement on the $x$; they can be any values you find convenient (as long as they meet the above two requirement)