Here's the complete list of codes and their meanings:

00 - Valid Ticket
01 - UTS Gate Fault (Invalid Tables)
02 - Wrong Type/Direction of use for this type of ticket
03 - BR only - no LUL validity
04 - UTS Gate Fault (Check Table Error)
05 - Technician signed onto machine
06 - Test Ticket
07 - Code Unreadable (Usually when ticket is upside down)
08 - Recoding Error
09 - Ticket Damaged
10 - Carnet Validated (Carnet Validator Only)
11 - Out of Date
12 - Not Valid Now (e.g.. OPTC before 0930, Freedom pass before 0900)
13 - Additional Fare Payable
14 - Not Valid, and is not excessable
15 - No onward validity
16 - Pass at Invalid station
17 - Excess/platform ticket at wrong station
18 - Station Permit at wrong station
19 - Start Date in future
21 - Ticket already used for entry
22 - Ticket already used for exit
23 - Carnet not validated on entry
31 - Invalid From OSI
32 - Invalid Into OSI
33 - Illogical Interchange through gates [1]
41 - Ticket used three times in quick succession at same station (entry-exit-entry or exit-entry-exit or purchase-entry-exit)
42 - Double use in one direction
51 - Already used for 1 journey (single) or 2 journeys (return)
52 - Pass Reported Lost or Stolen [2]
53 - Permit Reported Lost or Stolen [2]
54 - Possible Dumbell
61 - Too long spent making interchange
62 - Too long spent on journey (carnets only)
63 - Too long on platform (platform tickets only)
64 - Too long on excess (Fare-Paid tickets only)
65 - Entry time exceeded on platform ticket
73 - Ticket given back for possible emergency use (e.g.. substitute bus
service) and is not valid at this station
82 + 83 - Illogical Use of Ticket
90 - Gates set to reject this ticket type (normally child-lock)
99 - UTS Gate Fault (Check Time-out)

These codes come into four catagories :

[1] #33 is when, say you exit through Monument station and re-enter at
Tower Hill. The interchange is illogical, so won't accept your ticket.

[2] Pass is things like Staff/Dependant/Retired passes. Permits are
things like Freedom Passes.

Both can be intercepted if reported lost or stolen (retained by
machine, machine closes awaiting staff assistance. Code remains for
staff to decipher)

The above codes also apply on National Railways barriers, which are
virtually identical to the LU ones.

Tube Barrier Gate Error Codes

You know when you put a ticket through a barrier on the Underground and
"Seek Assistance" comes up on the display. Well, if you look on the
left- hand side of the display unit when that happens, you'll see a two-
digit code which the member of staff uses to work out what's wrong with
your ticket.

Note: On the newer gates, the code is displayed on the main barrier
head and can, afaik, be seen from either side just by looking
underneath the "Seek Assistance". This also applies to the Mark III and
Mark IV gates but not, for some reason, to the far-left set of Mark IV
gates (the Prestige ones).

 

History of the Challenge and other challengers
Zone 1 Alternative challenge
The official rules
List of error codes on barrier gates
Secrets of the Underground
Miscellaneous Facts of the Underground

Sillymaps