You can run the app in compatibility mode which will fix most apps. This basically tells the app that its running on a Windows XP machine.
Failing that you can install Windows XP Mode on the machine which will run a Windows XP VM on the computer and then install the app on the VM. This will run the application within Windows XP but display it on the Windows 7 screen.
The only way to fix the application would be to identify the bug(s) in the source code and correct them. If it is a vendor app they will need to provide you with a new version of the application.