It's done! Two indexing groups - Ancestry.com and The 1940 Census Indexing Project - have announced this week that they've completed 1940 census indexing. You can now search by name, rather than searching the documents page by page. Visit Ancestry.com or FamilySearch.org to use the index.
I decided to "test" the indexes using my ancestors. I was able to find one ancestor on both indexes but had to use different combinations. Ancestry.com had incorrectly added a space in my ancestor's name, while the volunteer indexer of the FamilySearch.org had missed a capital letter. Another ancestor turned up properly on both indexes despite my incorrect search terms. I had used Katherine - while the census listed her as Kate. Both indexes had clear mistakes: country names are misspelled on both indexes, although Ancestry.com's were more obviously incorrect (Austria does not begin with an S!). In both cases, the enumerator spelled the word correctly. In short, both indexes have problems, but FamilySearch seems to be a little better.
To both index sites, however, please add a correction option. I don't have a problem with you reviewing my corrections, but I'd have to see these errors passed onto a family tree.