  Sunyaev-Zel'dovich (SZ) surveys are promising probes of cosmology - in
particular for Dark Energy (DE) -, given their ability to find distant clusters
and provide estimates for their mass. However, current SZ catalogs contain tens
to hundreds of objects and maximum likelihood estimators may present biases for
such sample sizes. In this work we use the Monte Carlo approach to determine
the presence of bias on cosmological parameter estimators from cluster
abundance as a function of the area and depth of the survey, and the number of
cosmological parameters fitted. Assuming perfect knowledge of mass and redshift
some estimators have non-negligible biases. For example, the bias of $\sigma_8$
corresponds to about $40%$ of its statistical error bar when fitted together
with $\Omega_c$ and $w_0$. Including a SZ mass-observable relation decreases
the relevance of the bias, for the typical sizes of current surveys. The biases
become negligible when combining the SZ data with other cosmological probes.
However, we show that the biases from SZ estimators do not go away with
increasing sample sizes and they may become the dominant source of error for an
all sky survey at the South Pole Telescope (SPT) sensitivity. The results of
this work validate the use of the current maximum likelihood methods for
present SZ surveys, but highlight the need for further studies for upcoming
experiments. [abridged]
