I was trying to answer this question (here) and I found that I can't use Epilog with Show. consider this Example:
p1 = Plot[Sin[x], {x, 0, 4},
Epilog -> {PointSize[0.04], Point[{1, 0.5}]}]

p2 = Plot[Cos[x], {x, 0, 4},
Epilog -> {Red, PointSize[0.04], Point[{2, 0.5}]}]

Show[p1, p2]

It is clear that only Epilog of the first plot is taken.
Any idea why?
Thanks
Epilogs manually so I didn't include that. – Szabolcs Jan 22 '15 at 21:06