welcome, I see Mark has posted while I have been typing my response
, some of what I have said is still probably useful so here goes...
Please start by posting your FreeCAD "help about FreeCAD" data.
Secondly, if you attach a fcstd file showing an example of the problem, to your post, we would be more likely to give you a definite answer.
Did you model your shape first fully in Part and PartDesign workbenches, then select the final result and convert that to STL?
Is there any chance that you used the boolean tool in Mesh workbench? If so then don't. This is what happens under some circumstances if you use a boolean cut in Mesh workbench using meshes for the cut object and the cut tool.
Did you "import" a stl file at any point? Note that you can import a mesh as a mesh and keep it as a mesh (stl) or you could import and convert it to a solid. Generally importing stl files should be avoided where possible...in most circumstance because the format by its very nature looses a lot of information about your object. Round holes actually become regular polygons.
Here is a zipped up stl file as an example Please have a look at this and see if it works for you in your other software.
here is the fcstd file which created it.
OS: Ubuntu 12.04.3 LTS
Version: 0.14.2867 (Git)
Python version: 2.7.3
Qt version: 4.8.1
Coin version: 3.1.3
SoQt version: 1.5.0
OCC version: 6.5.0