As far as I know, there aren't a lot of differences between JDK 6 and JDK 7. At least, I haven't yet come across a difference (I coded with JDK 7 and with JDK 6).
A lot of computers run JRE 6 or JRE 7. Compiling my program using JDK 7 will narrow the number of potential computers that can run my application.
Is it generally a good idea to always program using JDK 6 and compile my program for JRE 6? Is this something common? Or is it generally a bad idea?