HELP: Support material prevents model from working correctly

I keep trying to make this print correctly, however the support material from the printer places supports inside holes where I am unable to take the support material out and prevents the pieces from fitting together.

3d Printer is a Makerbot Replicator 2 that uses PLA.

Any suggestions to prevent support material from being printed in these places?

If you are using Simplify3d you can manually place the supports (as opposed to having them automatically generated), thus avoiding the problem areas.