I have Project 2002/3/7/10 & 13 on my desktop. I’ve experienced a couple of issues only….
1. File association – clicking on an MPP plan – Windows will usually associate the last installed version to the mpp plan.
2. Visual reports, running Project 2007/10 with Office 2013 requires you to copy excel.exe and visio.exe into the Office 2010/Office 2007 locations to get them to be seen by Project 2007/10
3. Some HTML windows fail to load and cause project to crash, eg The Project Guide in 2007 – I think this can be fixed with a repair on Project.