How can I get all music "tags" to transfer when transferring an iTunes library?

Question

OK, here's my situation:  I have accumulated about 250GB of music on iTunes on a laptop running Windows 7.  The hard drive was running out of room, and I wanted to upgrade computers.  So I bought a Mac Book with 1TB of hard drive space.
To transfer my library (which includes about equal parts iTunes purchases and imported CDs), I copied the entire iTunes folder onto an external hard drive, and then used the "add folder" function on iTunes to add the entire library to my new computer.  I knew I would lose all data such as last played, most played, etc.  And I knew from past experience that merely transferring the iTunes folder, including the iTunes library file, to the new computer hard drive (without using the "add folder to library" function) would not mean that the new computer would automatically behave as if the exact same library from the old computer was on the new computer.  I hope I am explaining this right.
My problem/question is: many of the music files came over without some of the tags that were on the files in the old computer.  This happened with respect to some, but not all, of the imported CD files.  (I had used the MP3 format when I ripped these.)  The song titles are still there, but many of the tracks say "unknown album" for that artist or, worse, just say "unknown album" AND "unknown artist."  Because I have accumulated so much music over the years, it would take me quite a while to re-tag all he music files with all the missing info.   Again, I'm lucky to have the files, and my iPods containing the music have not yet been synced to the new computer, so I could just manually check what I had on the old iPods and re-add/re-tag the files that were problems.  I  know having such a large folder could itself be the problem.  But adding folders to the computer one at a time does not seem to help, as the "unknown" issue keeps happening even then.
So my conclusions are that one of the following has happened:  either there is another way to import a large library that I should try (Apple migration assistant, maybe?), or I somehow made the transfer from the old computer onto the external hard drive in the wrong way and I'm stuck with things as they are (which would not be terrible, just inconvenient) or there is some limitation in the software of music services that results in many "unknowns" showing up.  These were not obscure records, and iTunes/Gracenote recognized 99% of them just fine when I imported them, but I remember from using Windows Media Player that it was pretty hit-or-miss at times in terms of the right tags being assigned to songs.
Yes, I probably have spent way too much time over the years on my music.  But if there is something I can learn from this, I'd be happy to hear about it, either to fix things easily now or the next time I transfer music.  (Again, all the files had all the correct tags on my old computer, before I copied them.)  I thank anyone who replies very much, in advance!

Answer 1

Just to update: the solution above works.  I had tried to "import" all my files into the new computer rather than just copying and pasting the old iTunes folder into the new computer.  This second, easier, solution is much, much better than re-importing all the songs.  Seems like those little files included in an existing iTunes folder are very, very important!  Without them, I would have had hundreds and hundreds of "unknown" files to re-tag.  As it was, when I copied and pasted the existing iTunes folder into the new computer and opened iTunes, all the files were there, complete with all the date added/date played/number of plays/etc. information from my old computer.  (For some reason, this didn't work when I transferred from PC to PC, but that was several years ago and not a transfer to a Mac.)  I did seem to lose album artwork for a number of albums I had imported rather than purchased, and there was other cleanup to do on a small percentage of files.  But that was a vry small amount of work compared to re-tagging from scratch.  Thanks again for your help.