The only time I've ever had the "... is empty" error occur is when I've created an entity, and then try and tie it to an entity again. You will be given a dialog box asking whether you wish to create a new entity or tie it to the old one. If you create an new one, then the old one is not deleted but simply no longer linked in with the brush. This leads to an entity being "without a home" so to speak. The editor tells you this is the case by saying the entity is "empty".

To fix the problem select the error from the list, and press the "go to error" button. Now close down the error checker, and simply press delete. This will delete the entity. Do this for each and every entry in the error list (I'm afriad there is no way to do this in one), and your all sorted.

The other error about "...has unused keyvalues" is kinda as korn said. If for example you give a func_wall a direction on the compass thingy in entity properties. Some entities do not make use of all the keys in their properties (most new FGDs have weeded these out though) and so if you give that key a value, it will let you know that it was pointless by telling you so in the error list. Its not a critical error however, and will have no negative effects on the map, so don't feel you need to do through and remove unneeded values or anything.