Why is the melting point of propane lower than that of both methane and ethane?
Ok, let's first look at the trend...

$$
\begin{array}{c|c|c|c}\hline
\text{Chemical} &amp; n \text{ in }\ce{C_nH_{2n+2}} &amp; \text{m.p. / K} &amp; \text{m.p.}(n) - \text{m.p.}(n-1)\text{ / K} \\
\hline
\text{Methane} &amp; 1 &amp; 90.7 &amp; \\
\text{Ethane} &amp; 2 &amp; 90.4 &amp; -0.3 \\
\text{Propane} &amp; 3 &amp; 85.5 &amp; -4.9 \\
\text{Butane} &amp; 4 &amp; 133\mathrm{-}139 &amp; +50.5 \\
\text{Pentane} &amp; 5 &amp; 144.1 &amp; +8.0 \\
\text{Hexane} &amp; 6 &amp; 177\mathrm{-}179 &amp; +36.9 \\
\text{Heptane} &amp; 7 &amp; 182.2\mathrm{-}183.0 &amp; +4.6 \\
\text{Octane} &amp; 8 &amp; 216.0\mathrm{-}216.6 &amp; +33.7 \\
\text{Nonane} &amp; 9 &amp; 219.0\mathrm{-}220.0 &amp; +3.2 \\
\text{Decane} &amp; 10 &amp; 242.7\mathrm{-}243.9 &amp; +23.8 \\
\hline
\end{array}
$$

Using the mean for the alkanes with melting point ranges given (e.g. 136 for n-butane and 178 for n-hexane), it isn't clear there is any "great" linear trend. In fact it seems that the even number n-alkanes are on one curve and the odd n-alkanes are on another. 

There is a "general trend in that with increasing MW the MP increases. However the exceptions would seem to be both methane and ethane, not propane. Also it is obvious that a simple correlation with MW alone is not sufficient to characterize the trends. All in all I think one must be careful not to read too much into such trends without a very careful analysis.