There is confusion about the iPod Mini regarding multiple play lists.
Does it support them?

The user manual for the iPod Mini certainly gives the impression that
it does support multiple play lists.

"You can create as many playlists as you like using any of the songs
in your computer?s music library. Putting a song in a playlist doesn?t
remove it from the library.

When you connect and update iPod mini, the playlists are transferred
to iPod mini.  To browse through playlists, select Playlists in the
iPod mini main menu."

Source: http://download.info.apple.com/Apple_Support_Area/Manuals/iPod/0190191_iPodmini_UG.pdf
(page 27)

Does this help?

It certainly does... have one of these myself and you simply drag and
drop whatever playlists you require from iTunes to the iPod and they
show up on the player.

Thanks!