My lights have gone crazy! A real mystery?

I have a 1995 Olds cutlas supreme with 178,000 miles. We replaced the turnsignal module (I think that is what it is called, every dealership has called it something different) due to my break lights and turnsignals were not working properly. Now that we have it hooked up the break lights work, but if you turn on the right signal, the hazards come on, or if you turn everything off the left signal light comes on, but does not flash. Sometimes, the whole left side, with the exception of the break lights, doesn't work. All the bulbs have been checked and are ok and the proper bulbs. All the fuses are ok. Their was only one way to unhook the old part and install the new one, so I am pretty sure it is in properly. Any suggestions, could the new part possibly be defective?