Yes, make sure the PATH (IE, Z:/FOLDER NAME) is the same on every computer you put it on.
The biggest piece of advice I can give is keep your computer folders a mess and have everything in one single folder, but then organize and separate everything inside of Premiere with the bins.
A Premiere Pro project file *.prproj is nothing but a road map to where the files are. It is a glorified EDL (Edit Decision List). If you move the project around on computers, it has to re-route that road map to match. If you put everything into a single folder on your hard drives, if you link the first file, it will automatically re-link all of the files. If you have a ton of sub folders, you will have to re-map to each folder, hence - use a single folder in Windows and all your bins inside Premiere.