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Duplicate is the command you want. Try this:

repeat with theAlbum in randAlbums
    duplicate (tracks of library playlist 1 whose album is theAlbum) to thePlaylist
end repeat

Within the iTunes interface add is used to add a new track to the iTunes library using a file system path, while duplicate is used to place a reference to an existing track in a playlist.

When the add command is used iTunes will eventually figure out that the track is already part of the library and do what you want, but not before it reads the file's metadata, schedules it for album art retrieval, etc. All of this amounts to a pretty slow operation so if you're using it within a loop for a large number of tracks iTunes will slow to a crawl.

Duplicate performs a native database lookup and adds the results to the playlist all at once so it is very fast.

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Try:

copy the_track to end of playlist thePlaylist

instead.

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Try changing that line to:

add (get location of the_track) to playlist thePlaylist

or, if thePlaylist is already a playlist reference (instead of just the string name of a playlist):

add (get location of the_track) to thePlaylist

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Applescript is really weird...but checkout the scripts here dougscripts.com

Looks like he uses duplicate and not add when adding to a playlist. I'm looking at the One Song From Each script

Hmmm...how about?

add (a reference to the_track) to playlist thePlaylist