Importing music from my Microsoft Zune into iTunes?

Go to iTunes > Preferences > General > Import Settings: Import using:

Any files already in MP3 AAC or AIFF will play with no issue as you have already discovered. Delete the WMA files but do not choose to move them to the Trash. Instead, import them a second time after having made the Import Settings as shown; they will be converted this time. There are third-party apps that will do the job also (such as Audacity) but you can accomplish your goal with iTunes.

Try the operation through the File > Add to Library >

rather than drag and drop.

There seems to be a glitch with this method for you (even though it ought to work as outlined). Be sure that there isn't a step you have left out. You can accomplish the same task by using Garage Band, although it will be a painstaking operation if you have several gigabytes of files. You can open Garage Band and make a new project; drag one WAV file into the arrange window and allow it to be prepared; there is no need to play it through. Go to "Share" in the GarageBand menu bar and select 'Send Song to iTunes'. You will then be asked to select a file format; choose MP3 as the safest format because you want the song to be played not only in iTunes but (probably) in an Apple portable device as well, such as an iPod or iPhone. The application will export the song to iTunes into a Playlist under your name. As stated earlier, this would be very laborious with several gigabytes worth of files but it will work; perhaps you could do only a few albums at a time. I stated earlier that Audacity would also do the job. It is an open-source (free download) project available from this URL:

http://audacity.sourceforge.net/download/beta_mac

It would be every bit as painstaking as the GarageBand method but since the standard iTunes operation isn't working for you at least it provides a workaround. There might be someone else in this forum who could provide insight that is missing here.