I experience both problems, books without covers and "ereader storage errors", but have not had problems with either lately.
Book covers - You need to do a conversion to make sure you your cover will transfer correctly. Just do a epub to epub conversion and your cover problem should go away. I like right and left margins so I always do a conversion changing the margings from 5 points to 20 points anyway.
"E-Reader Storage Errors" - Since I have taken the precaution of waiting a few seconds after each job is processed when downloading and then again after ejecting the device from calibre I have yet to experience another "e-reader storage error" message.
I have a couple of hundred books I manage through calibre and I would have a hard time getting along without it now. Although, I did have to go through an initial learning curve which I accomplished by reading posts on the calibre forum.