I recall hearing "Nothing Bad Ever Happens" and "Who Do You Want To Be?" on the radio, but I think that was just my local new wave DJ's choices. According to Wikipedia, "Wake Up It's 1984" was the only single released.
What are the three hits you're referring to? I'm sure "Weird Science" and...
EWF - Fantasy is an interesting one. In the single version, it goes to the bridge and doesn't come back. For the album version, they go to the bridge once, then tease a bit of the intro & verse at 2:26, but jarringly jump right back into the bridge and stay there.