Here are some examples of how album information should appear. Note that your missing artists problem is specifically addressed in item 4 under the heading For a Compilation album (a various artists album): below.
The reason that an artist is not showing up in the Artists menu is because the album is listed as a "compilation" album, that is, an album by various artists.
The index of artist names on the iPod is achieved by using the Album Artist field (there's a specific tag - or field, for it in each song). On a one-artist album, if the album artist field is blank, iTunes uses the Artist field to index the artist's name. On a "various artists" album, the Album Artist field will have the artist name as Various Artists, so every track on that album will be listed in the artists menu, under Various Artists.
The screenshots below demonstrate how the album information should look in your iTunes Library, according to the type of album, in order for both iTunes and iPod to index everything correctly:
For a single-artist album:

- In the example above, all the songs on the album are selected (the grey background titles to the left of the larger box). The large box is displayed by leaving all the tracks selected and clicking on Edit/Get info
- shows the artist name (Dire Straits)
- shows the artist's name. Because every song in the selection is by the same artist, this also states Dire Straits
- Notice that album artist is blank. With a single-artist album, this is acceptable. It may contain the artist's name, this is also acceptable
- the compilation flag must be off (not ticked). This is true, even if the album is a compilation of songs by one artist, that is, a greatest hits album. If this flag is set on, on this album, every track will be listed separately on your iPod, so that's probably what's happening with the Adele album
For a Compilation album (a various artists album):

- In the example above, all songs on this compilation album are selected and the large box shows you the Edit/Get Info panel:
- this shows you the album artist, and since each song is by a different artist, the album artist is Various Artists, and it shows the album title: Crate Diggin' Fever
- the artist field states mixed because there is a mixture of artist names
- the album title again. This where you can edit the tile, if you need to
- the album artist states Various Artists. In order for this album to display correctly on an iPod, this field must contain the text Various Artists. The reason you have artists missing on your iPod is because the artist will only appear in the artist menu if that artist also has a single-artist album on your iPod. If you would like further explanation on this, please ask
- the compilation flag must be on for a various artists album. But if it is on for a single-artist album, it will split every track into its own album on your iPod
See the additional post, which will, be put up in a few minutes.