I have converted applications from LabView 6.02 to 7.1 without any problems.
Note that
a) 7.1 does not support win98/ME. So if your target application is win98, do not upgrade the application.
b) If you are using data acquistion, your application needs traditional Nidaq (7.1 and higher) be installed on the target machine, unless you are willing to convert your daq vi's to DaqMx. Note also Nidaq 7.1 and higher does not support some old daq hardware (like PCI-1200). So make sure your daq hardware is still supported.
c) If you were using serial communications, 7.1 uses serial VISA, and your vi's will be converted accordingly. Normmally there should not be a problem with that. You may have to install the VISA runtime engine (it comes with LabView) on the target machine