I have solved my dilemma thank you. I was given the tip to download the free App, MplayerX whilst brousing other questions like this one. And it has worked for me. Thank you! This is my first question and I am trying to do it right. This is a quote of the help I received. Oh by the way, .mp4 files are a breeze for QuickTime, it's the .MPEG-4 that is a problem.
"I have this same issue. Now I have switched to using MplayerX which you can get on the App Store. It plays everything, uses a lot less energy than Quicktime (as per Mavericks own activity monitor) and if you are watching a video, but close the app, it will re-open the video where it left off when you open the app again. It's so much better than Quicktime and looks nicer than VLC with no borders on the video."