A caution (assuming it was issued in the UK) WILL show up on your Disclosure and if issued for shoplifting is a potentially disqualifying factor from using the US VWP BUT as it is not a conviction does not neccessarily constitute 212(a) ineligibility for a visa. Failure to declare the caution on your ESTA application however is an offense that WILL result in ineligibility and disbarment from the USA.

Failure to declare a caution may catch up with you anytime down the line. I know of an airline captain who failed to declare a caution he received many years previously but was stopped (despite holding a valid C1/D visa and operating dozens of times to the USA under the visa) and subjected to expedited removal proceedings and a 5-year bar after operating a flight to the USA simply because he had failed to disclose the 20-year old caution on his visa application form years previously.

The US Embassy has advised crewmembers who have cautions on their record to carry copies of their Disclosure statements with them to visa interviews and also when traveling to the USA in order to demonstrate that there is no ineligibility. While I am neither an immigration lawyer nor consular officer, I believe this to be very sound advice. Declaration of a potential ineligibility and presentation of evidence to overcome the presumption of ineligibility is the quickest and least painful way to deal with this kind of circumstance.

At the end of the day, it is probably not worth the risk to attempt travel using an ESTA issued via misrepresentation of material facts. 90% of those who do not delcare previous cautions probably slip through undetected but the consequences for the 10% who are caught could have long lasting effects on one's life.