  We give examples of two dimensional normal ${\mathbb Q}$-Gorenstein graded
domains, where the set of $F$-thresholds of the maximal ideal is not discrete,
thus answering a question by Musta\c{t}\u{a}-Takagi-Watanabe.
  We also prove that, for a two dimensional standard graded domain $(R, {\bf
m})$ over a field of characteristic $0$, with graded ideal $I$, if $({\bf m}_p,
I_p)$ is a reduction mod $p$ of $({\bf m}, I)$ then
  $c^{I_p}({\bf m}_p) \neq c^I_{\infty}({\bf m})$ implies $c^{I_p}({\bf m}_p)$
has $p$ in the denominator.
