I have a paper giving an irreducibility test (and factoring "algorithm", in some sense of the word) for formal power series over a PID, which should eventually appear in Trans. of the AMS.  In particular it applies to $K[[X]][[Y]]$.

See Theorem 1 of http://arxiv.org/abs/1107.4860

In essence: Write any polynomial $f$ in $K[[X,Y]]$ as a polynomial in $Y$ with coefficients in $K[[X]]$, and let $f_0$ and $f_1$ be the coefficients of $Y^0$ and $Y^1$, respectively.  Then $f$ is irreducible in $K[[X,Y]]$ if and only if either (1) $f_0 = 0$ and $f_1$ is a unit in $R[[X]]$, or (2) $f$ has a unique factor in $K[[X]][Y]$ with constant term not a unit in $K[[X]]$.