Step 1: Understanding Oxidation with $KMnO_4$:
Potassium Permanganate ($KMnO_4$) is a strong oxidizing agent. In acidic medium, the permanganate ion ($MnO_4^-$) itself gets reduced to the Manganese(II) ion ($Mn^{2+}$).
Reaction: $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$.
Step 2: Analyzing the Options:
(A) $S^{2- \rightarrow S$:} Sulphide ion is oxidized to elemental Sulphur. Correct. ($H_2S \rightarrow S$)
(B) $Mn^{2+ \rightarrow MnO_2$:} This is an oxidation of manganese from $+2$ to $+4$. However, $KMnO_4$ acts as an oxidizing agent and gets \reduced to $Mn^{2+}$ in acidic medium. It does not oxidize $Mn^{2+}$ further to $MnO_2$ in standard acidic conditions (that is the reverse of what happens to permanganate). In neutral/alkaline medium, $MnO_4^-$ reduces to $MnO_2$. But the question specifies "acidic medium" and asks about the oxidizing \property (what it does to others). $KMnO_4$ cannot oxidize $Mn^{2+}$ because it reduces \to $Mn^{2+}$. This reaction represents the product turning into an intermediate, or is chemically incorrect in this context. Thus, this change is not correct.
(C) $SO_3^{2- \rightarrow SO_4^{2-}$:} Sulphite is oxidized to Sulphate. Correct.
(D) $C_2O_4^{2- \rightarrow CO_2$:} Oxalate is oxidized to Carbon dioxide. Correct.
Step 3: Conclusion:
Option (B) is incorrect because $Mn^{2+}$ is the reduction product of $KMnO_4$ in acid, not a substrate it oxidizes to $MnO_2$.