Slicing adds holes/cracks to my object I recently got started in 3D printing but here's an issue I can't seem to find a solution for (I don't know what exactly to look for).

Here's what I did:


I used InkScape to convert an emoji in to a svg and imported it in to Blender
Used the Solidify modifier to make the curve a solid and converted it in to a mesh
Extruded the mesh a bit, fixed a few non-manifold vertices and erroneous faces and saved the whole shebang as STL
Imported the STL in to my printers software: 

After slicing it looks like this: 



Is the software making a mistake during the slicing? Or is my mesh screwed up?

I have a FlashForge Finder and using the software that came with it: FlashPrint.

Edit: I uploaded everything to Thingiverse for those who are interested.
here is just a addenum to Tom van der Zanden's answer

this is (an example of) what you may design - nice object with virtual outline, and virtual fill
so this is what you see (and what you potentially expect)



but here is what you get (and probably not really expect)



red parts are the areas which are not covered by fill because nozzle cannot reach there

solution is 


to redesign your object in smart way or
to use smaller nozzle or
to use smarter app (like Slic3r)


and of course you can use all 3 options together to get best results ;)

EDIT
here is simple explanation why smarter app could do the thing


and here goes the difference



green parts are new covered areas

not much but somthing extra