There is a problem with the stroke of the glass: at this small size, it seems to be less black than the parasol's stroke...
This is because in the parasol, each stroke is done twice. You have the black outline of the entire parasol and then you have each segment with its own outline which overlays the first outline. Even though the strokes have the same width and are exactly on top of one another, the fact that each stroke has its own antialiasing fringe and these fringes add together results in the stroke appearing thicker than it should at small sizes. This is a common problem for most vector editors with antialiased display, not only Inkscape; for example Adobe SVG plugin also shows your file with the parasol outline darker than the glass if you zoom out far enough.
So, to fix it, you can either remove the double stroke (so that overlaying segments have only fill and no stroke) or export it at a larger size and then resize the bitmap.