I don’t think that you will have any technical issues. You can save the file as a previous version. This should work without error. Also, I am assuming that you are talking about the non-server version since you can’t cross-post between server versions.
However, the issue that comes into play is the functionality – each version has new features, capabilities and formatting that will be lost.
I am working with a client and some of their other vendors who use MSP 2003 in a non Server environment; we consistently are sharing files in compatibility mode. Generally the files appear to work well together. However, we have had some problems with lookup table values disappearing for custom fields and a couple other smaller problems. Some problems dissappeared by first saving the file in XML format and re-opening in MSP.
The bigger issue was the pain in always having to remember the audience who would using the file and therefore what format to save it. We solved the problem by convincing all parties to upgrade to 2010.