I've been researching for a while, and my Thaumnomicon looks pretty full. How can I know when there's nothing left to research? Is the only way throwing every type of essence at the research table in enough quantity or is there a better way?
There is no way to tell in game when all of the research is done. The easiest way to do this is to visit one of the many wikis and see what the complete list is and compare it against what you have.
To address what you mentioned about essences as well it should be known that there are recipes in the table that can not be unlocked by researching just on essences alone. To my knowledge this is only hinted at in the game and would be something you could stumble across by knowing certain items were added into the game via Thaumcraft (I mention this part because people are coming across quite a few of these mods via packs like Feed The Beast where it can often be confusing what is part of which mod).
This only stands as things currently are in Thaumcraft (v3.0). Research is one of the things mentioned by the creator that he is looking to change in the next major release (v3.1).
Hope this helps