Imported playlists but not all songs will import

You should transfer your complete iTunes folder (in one piece), which would include all of your media files and your iTunes library database (where the supporting data such as playlists, ratings, play count, date added, etc. are stored). Then, iTunes on the new Mac looks like iTunes on the old Mac, with all of your songs and playlists, because you are using the SAME library; you are not adding your media files to a new library.

If you want more info on how to do this, instead of trouble-shooting your playlist export/import issue, please post back.

This document describes how to back up your iTunes folder to an external drive (or a USB flash drive if large enough).

Back up your iTunes library by copying it to an external drive - Apple Support

To summarize, the first section consolidates your media files into the iTunes Media folder inside your iTunes folder (the one inside your user account Music folder). For a Mac user, if you are using the default settings, all of your media files (for iTunes) should already be in that iTunes Media folder, but it does not hurt to do it, just in case. The second section copies the iTunes folder to an external drive. The third section restores the iTunes folder, in your case to the new Mac. You should do this part with iTunes NOT running. You are replacing the existing (new) iTunes folder was on the new Mac with the iTunes folder from the old Mac. When you run iTunes, it uses the iTunes library and data from the old Mac, complete with all songs (and other media) plus the supporting data, such as playlists, ratings, play count, date added, etc.

Sorry, I forgot to include the link to the document. I edited the post to include the link. Also shown below.

Back up your iTunes library by copying it to an external drive - Apple Support