Let $G$ be an algebraic group acting on a scheme $X$. Then $f: X \to Y$ is called a categorical quotient if it is constant on $G$-orbits and every $X \to Z$ constant on $G$-orbits factors through it in a unique fashion. We call $f$ a 'good' categorical quotient if:

1) $f$ is a surjective open submersion (i.e. $Y$ has the quotient topology).

2) for any open $U \subset Y$, the induced map $\mathcal O_U \to (\mathcal O_{f^{-1}(U)})^G$ is an isomorphism.

Does anyone know an example of a 'bad' categorical quotient (by which I mean...well...a not good one).