I design my parts in SolidWorks 2015, but I download stuff from Thingiverse occasionally and these are the parts that usually give me trouble. The part I'm showing was a download.

Although I did make a part myself that was basically a flat plate with some through holes and Makerware sliced it such that it printed the holes and nothing else - the inverse of the part. And that was built in SW, saved as an .stl and opened in Makerware. I tried flipping it sideways and other holes did the "slot thing" I mentioned. I ended up just deleting most of the holes to get it to work.

Come to think of it, I made all the holes with Hole Wizard (which I usually do since it's easy) so maybe something's buggy about that...