When I upgraded to Ubuntu Karmic, I reloaded Eclipse from the repositories, and everything seemed to be happy. Except my cherished autocomplete!
I dug around online, and found this site; the solution wasn’t in rebuilding my project, but rather in the comments.
Go into Window > Preferences > Java > Editor > Content Assist > Advanced and make sure “Java Proposals” is checked.
If you find that some members are missing, you may need to muck with some of the other checkboxes in that screen. However, when I checked “Java Non-Type Proposals”, “Java Proposals”, and “Java Type Proposals”, every member was duplicated in the list. That’s not damaging, but it is irritating. Just leaving “Java Proposals” checked seems to have made everything happy once again.