Vibration on acceleration can be caused by several things. Seized universal joints are very common for this problem. To check them properly, the drive shaft has to be removed and each joint operated through its entire range. Any tightness or binding means a bad joint.
Engine running problem also feel very similar to a vibration very often. This engine is notorious for bad ignition coils and they tend to miss on acceleration. The best way to test these are with a scan tool that can read cylinder balance, such as the Ford IDS. Reading mode six data will also often show a misfire, long before a check engine light is set.