Step 1: State the IUPAC criterion for transition metals.
A transition metal is an element whose atom has an incompletely filled d-subshell, or that can give rise to at least one stable ion with an incompletely filled d-subshell.
Step 2: Check Cu, Ag, and Pt.
Cu ground state is [Ar]$3d^{10}4s^1$; however, Cu$^{2+}$ is [Ar]$3d^9$ (incomplete d). Ag$^+$ has $4d^{10}$ but Ag$^{2+}$ is $4d^9$ (incomplete). Pt forms Pt$^{2+}$ and Pt$^{4+}$ with incomplete 5d configurations.
Step 3: Check Hg.
Ground state of Hg is [Xe]$4f^{14}5d^{10}6s^2$. Its most common and stable ion is Hg$^{2+}$: [Xe]$4f^{14}5d^{10}$, which retains a completely filled $5d^{10}$ subshell. No stable Hg ion has an incomplete d-subshell.
Step 4: Conclusion.
Because all stable Hg ions have a filled $d^{10}$ configuration, Hg fails the IUPAC criterion and is not a true transition metal.
\[ \boxed{\text{Hg}} \]