What type of graph can be hepful to explain the type of errors that should be used?
You are saying: $y$ is regressed on $x_1$ and $x_2$, say, and you think it would be better to use cluster errors since you expect $y$ is correlated with abilities for each person.

First, $y$ is naturally correlated with the error term $u$ (if you mean the error term by "abilities") because $u$ is a part of $y$. You have no problems with that; $y$ is always strongly correlated with $u$. It also has nothing to do with cluster errors.

If you happen to mean cluster standard errors (SE) by "cluster errors", and if you are saying that you would use cluster SE because $x_1$ is correlated with $u$, I would say that the regressor-error correlation (endogeneity) has nothing to do with cluster SE, what so ever. Cluster SE provides valid inference when the the error term show within-cluster (auto)correlation.

Please enlighten me if I misinterpreted your question.