Why does the reaction between potassium permanganate and oxalic acid result in a yellow/brown solution?
The reaction between $\ce{MnO4-}$ and $\ce{C2O4^2-}$ is performed under acidic conditions. 

In acidic conditions only, $\ce{MnO4-}$ gets reduced to colourless $\ce{Mn ^{2+}}$ as, $$\ce{MnO4- + 8H+  +5e- -&gt; Mn^2+ + 4H2O}$$

But if you don't maintain proper acidic condition of the medium, it continuously absorbs $\ce{H+}$. Eventually, due to lack of protons, it gets reduced to brown coloured $\ce{MnO2}$ under neutral conditions, where it needs less no of protons to get reduced than acidic conditions, as $$\ce{MnO4- + 4H+ + 3e--&gt; MnO2 + 2H2O}$$ That's why you see the brown colour which is due to $\ce{MnO_2}$.