After quite a bit of searching (and an e-mail to Andy Looney, creator of Chrononauts), I was able to piece together the following:
Chrononauts First Printing
While this was the initial release, it did feature a number of art changes from the beta version, notably the beta card back was replaced with the one used in all subsequent editions.
Chrononauts Second Printing
Buried in the July 18, 2002 Wunderland Weekly News (the company's newsletter at the time), they note the following changes were introduced in the second printing:
- The box has been revised. The art on the front and top panels has been reversed, and several new bits of info have been added (Origins Award winner, Parent's Choice winner, Second Printing, Patent Pending, etc).
- 1962 will henceforth hinge on an "OR" instead of an "AND". This makes World War III and the ÜberParadox much easier to create, and to sustain, which will hopefully give Squa Tront (and Zane Reenak) more of a fighting chance. (It also makes it more satisfying to flip 1943 and 1957.)
- The Obvious Forgery of the Mona Lisa now sports a handlebar mustache.
- A note about Killing Time has been added to Fast Forward.
- The incorrect Time Index on the Marijuana Legalized card has been fixed.
- The teeny-tiny tick mark missing from the Rongo-Rongo Tablets has been restored.
Chrononauts Third Printing
The card list for the third printing has a few notes about what has changed with this version compared to the second printing:
- 8 Reverse Fate cards (down from 9)
- 1 Restore History card (down from 4)
- 2 new Artifact cards
- Jade Statue of Tirade
- German Cake
- The concept of Gadget cards are introduced with 2 new cards
- Really Fast Time Machine
- Teeny Tiny Time Machine
Rather than calling it the fourth printing, Looney Labs called this version v1.4 (as can be seen from this photo). The card list for this version noted the following changes:
- 4 new artifacts were added (increasing the total card count from 136 to 140)
- Beatles Reunion CD (Artifact)
- Live Triceratops (Artifact)
- 1945D: Tokyo Nuked (Patch)
- Restore History (Inverter)
- Bigger, better box
- Bigger, better rulesheet
- A Fast Forward was changed into a Reverse Fate
Additionally, the inverter cards added icons indicating which linchpins they could be used for in either Early American Chrononauts or The Gore Years expansion. For instance, Halt Attack notes that it can be used to flip the expansion's 2001 World Trade Center Attack linchpin.
As of this writing, Board Game Geek lists the version after v1.4 as the "Second Edition". I could not find anything about the changes with this version, so I e-mailed Andy Looney and got the following response:
The most recent version of Chrononauts is what we call v1.5, which differs from 1.4 only in the design of the box itself. There is no v2.0 of Chrononauts.
So according to the creator himself, there are no changes to any cards in v1.5 and the only difference is the new box cover.
Other Promo Cards
While we're at it, a number of promo cards eventually did wind up included in later versions (such as German Chocolate Cake), but there are two that never were (and are still for sale in Looney Lab's web store):