How to fool the plot inspection heuristic?
Speaking from experience, when trying to figure out the growth rate for some observed function (say, Markov chain mixing time or algorithm running time), it is very difficult to tell factors of $(\log n)^a$ from $n^b$. For example, $O(\sqrt{n} \log n)$ looks a lot like $O(n^{0.6})$:


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For example, in "Some unexpected expected behavior results for bin packing" by Bentley et al., the growth rate of empty space for the Best Fit and First Fit bin packing algorithms when packing items uniform on $[0,1]$ was estimated empirically as $n^{0.6}$ and $n^{0.7}$, respectively. The correct expressions are $n^{1/2}\log^{3/4}n$ and $n^{2/3}$.