I have just discovered that there are data unexpectedly missing from the 1820 Census Index (CD-314).  For reasons known only to the producers of this database and/or the CD, all surnames beginning with letters "A" through "E" and some "Fs" from Tennessee counties are missing from the CD.  The Tennessee records start somewhere in the "Fs."  (Actually, there is one record in the "Bs," but under the circumstances, that is hardly worth mentioning).  To give you an appreciation for the volume of records that must be missing, there are over 1500 records in TN for surnames beginning with "G," and surnames beginning with "G" are much less common than those beginning with letters "A" through "D."  In volume, we are probably talking about roughly half the Tennessee records.

After making this discovery, I decided to check the other states, with these results:

SC has only 14 records for surnames "A" through "D," none for "E";  and, as with TN, the records commence "normally" somewhere in the "Fs."

MS has only 181 records for surnames "A" through "E"; and, as with TN, the records commence normally somewhere in the "Fs."

These appear to be the only states affected.  The records for TX and WI are somewhat scanty and irregular, but this appears to be because TX and WI were still territories in 1820 and mostly unsettled, at least by Europeans.
 

In summary, the states effected in 1820 by the missing records for surnames beginning A through F are:

MISSISSIPPI, SOUTH CAROLINA, and TENNESSEE

NOTE:  These deficiencies also appear to afflict the online version of these databases at GenealogyLibrary.com.  Ancestry.com is also lacking the TN records, but appears to have some SC and MS records, but I haven't tested these thoroughly.  An easy test for this deficiency is to do a search on BROWN or CLARK or DAVIS, which are extremely common surnames in the United States.  Any state without these surnames must have a deficient index.

UPDATE (11 Jan 2004):  It appears the new indices online at Genealogy.com do not have these flaws.  I haven't checked exhaustively, yet.

I've just discovered that the 1840 Census Index (CD-316) has the opposite problem as the 1820 disk.  For reasons I'm beginning to suspect, the producers of this database and/or the CD have omitted records, only in this case, it's the surnames beginning with letters in the latter part of the alphabet, namely, the mid-H's through Z.  Again, the volume of missing records comprises roughly half of the expected records for the state, which in this case is, again, Tennessee.

As for the rest of the states, given the nature of the software interface, it is far more tedious to test for missing names at the end of the alphabet than at the beginning, so I have only checked Tennessee thoroughly.  For Tennessee, there are only 13 records for surnames beginning with "I" through "Z"; normal records appear to drop off in the "H's."  What I have done for all the states is to check for "Williams," which is the most common surname in the U.S.  If an entire state has no Williamses in its census, I think we can figure that state's data are similarly afflicted.  <time passes>  Well, it turns out only Tennessee is effected.  (HI and NM have no Williamses, but this lack is due to cultural differences; their records otherwise appear to be OK.)

This anomaly serves as a further warning that other years may be effected and perhaps with anomalies different from the ones so far discovered.  So, if you are tearing your hair out because you can't find someone you know must be there, invent a little test to see how complete the database for that state or county is.

In summary, the state effected in 1840 by the missing records for surnames beginning in the mid-H's though Z is:

TENNESSEE

NOTE:  The 1840 Tennessee database at Ancestry.com also cuts off at the H's (info courtesy of Debby McCoy, 14 Nov 1999), so both companies must have bought their data from the same flawed source.

I've just discovered that the 1800 Census Index (CD-312) has most of the records from Lincoln Co., NC, missing.  There are only 23 records for this county.  The database at GenealogyLibrary.com is similarly afflicted.  FYI, the surnames present are:  CARPENTER, DEAL, DURR, ESPEY, HOGGINS, HOKE, JOHNSTON, LUTZ, MASTER, McKEE, McKESICK, McLESTER, MILLER, NORMAN, PRICE, RUTLEDGE, and YOUNT.  Some other counties appear to be affected as well (e.g., there is only one record for Letchfield Co.), but I haven't checked them all.

I have just discovered that the 1830 Census Index CD contains exactly one record for Mississippi.  The same flaw exists in the indices at GenealogyLibrary.com and Ancestry.com.  The AIS index at Ancestry.com has 725 records, all from Natchez, Adams Co., MS.

The 1800 Census of Kentucky was destroyed.  On the 1800 Broderbund CD, tax lists are substituted for some counties.  In the case of Jessamine Co., there are some names, which may lead you to believe the county is covered, but it is not.  There are only 43 names for Jessamine Co., one surname starting with the letter "B" and 42 surnames starting with the letter "M."