I'm using 2008 PP on Mac. I need to produce a presentation then email the file. Am I safe with this old version? Will there be any problem with others opening the file and playing the slide show? Or opening with a tablet? Or, should I upgrade? Thank.

Should not be a problem. The newest version is superior BUT to your concerns, there should be no issue opening PPTX files from your 2008 files on any new device provided all files are set up correctly in the first place (having nothing to do with the version), sending files BACK to you might lose some formatting or animations. Potentially minimal loss or in the case of a particular animation that might use a new exit or entrance that you don't have the entire thing could lose it's punch.