To confirm how you are checking for the songs in iTunes... If the iTunes sidebar is not visible, from the menu bar, under View, select Show Sidebar.
In the sidebar, find the iPod under DEVICES. Click the small triangle to the left of the iPod to drop down its content list (indented below the iPod). If you are syncing a playlist to the iPod, it should appear there, on the content list. You can click on the playlist there to check for the songs (to the right). If you are only syncing the songs from the playlist (not the playlist itself), click on Music on the iPod's content list to show all of the iPod's songs (to the right). Confirm the songs you are looking for are on the iPod.
Is that how you checked for the songs and the playlist on the iPod using iTunes? What method do you use to load the iPod, the manually manage method or automatic syncing?