Kolmogorov-Smirnov was intended for continuous distributions.

The K-S test statistic has the same distribution under all continuous distributions. So if the distribution itself is not continuous and you do a level α test with the assumption of continuous distribution, the actual level of the test will be lower than α. In other words it would get more conservative.

So you would then need a way around it to get your critical value like for example simulation.

However it seems that recently an R-package was developed, to use K-S for discrete distributions

http://cran.r-project.org/web/packages/dgof/dgof.pdf

I only glanced over it a bit, but it seems to make use of Monte Carlo simulation for the p-value, should the distribution be discrete.

Kolmogorov-Smirnov was intended for continuous distributions.

The K-S test statistic has the same distribution under all continuous distributions. So if the distribution itself is not continuous and you do a level α test with the assumption of continuous distribution, the actual level of the test will be lower than α. In other words it would get more conservative.

So you would then need a way around it to get your critical value like for example simulation.

However it seems that recently an R-package was developed, to use K-S for discrete distributions

http://cran.r-project.org/web/packages/dgof/dgof.pdf

I only glanced over it a bit, but it seems to make use of Monte Carlo simulation for the p-value, should the distribution be discrete.

K-S statistics is based on the Smirnov's theorem which has the following statement: if  r is random variable with continous distribution and F(x) is its cdf then random variable F(r) has uniform distribution on interval [0, 1]. That's why K-S statistic has distribution that doesn't depend on distribution of input set if it is continous. If we apply K-S test to random variable r with discrete distribution then K-S statistics will have distribution that depends on the set of values of r. Smirnov's theorem will not be hold for discrete case.