I don't know if this is a known issue or indeed where the problem may originate but I imported a couple of Eagle components to see what does and doesn't work and had a problem with the text.
On each component I tried (I only did 3) the right hand side text on PCB outlines was upside down - the left was fine. (ie say a 74 series chip labeling on pins 1-7 OK pins 8-14 upside down)
Also on one the text underneath was corrupt - all there - but the font mangled. (It could easily be a font compatibility issue)
The ones I tried were from different libraries downloaded directly from the home site.
Actually using the converter is amazingly simple so a thumbs up anyway.
It isn't a big problem as the text can be corrected and its great to have this facility for the odd component - I just thought I'd mention it.
I have had similar problems. I think they are just due to differencies in format. I always just edit and clean up the import. I sometimes have found that some layers come in on the wrong layer etc..
It looks like we're kind of stuck with this issue, because Eagle doesn't provide a way for us to get the correct name orientation out of the Eagle design data.
One thing though that might help improve things for you, is to use the 'text readable' switch. Go to Settings, Design Options, and tick the box 'Adjust Text Rotation'. This forces all text to be drawn so that it is readable from bottom or right, so at least you shouldn't get names upside-down.
The alternative is to go ahead and tidy up the symbols yourself anyway, which often doesn't take too long and is in any case a good deal quicker than creating the symbol from scratch.