What makes a 'good musician' seems very hard to define. Autumatically taking into account that everyone's taste is different, I'd say it would be a mix between being technically proficient, writing accessible music, and being able to write original songs and play them to a good standard. Any of these three would work, though a mix would be better.
Take ABBA, for instance. Benny and Bjorn - I would say - cover all three bases. They have a very high understanding of the geography of music theory [just look at the score for Chess] but were able to write very popular songs using their knowledge, playing around with different ideas to what pop music had seen up till that point.
Take another end of the scale - a composer like Ligeti or Bartok. A lot of their stuff was considered off the wall and cacophonic, but given their understanding of music theory and originality this would also make them good musicians.
So who isn't a good musician? Quite simply, someone like Britney. Atomic Kitten etc. These people don't write their own music and can hardly sing. They're just results of a manufacturing process.
Now for the difficult one - Lacuna Coil. Would they be considered good musicians? I'd have to argue that they're not. Cristina can't sing [her live vocals are poor and she's hammered with autotune on disc], their song-writing is not original and their 'accessible' songs are not that good [again, personal opinion]. They are very hard-working musicians which is why they've got to where they are.