A year ago, I was caught shoplifting and was arrested on a burglary charge. My lawyer later managed to get the burglary reduced to petty theft. In court, the petty theft and burglary charges dismissed. He pled me no contest to Trepassing (CA penal code 602(k)).
I have since left the USA back to my country for good. I would like to apply for a tourist (B1) visa to visit my friends back in the USA. Will this record make me ineligible to apply for the visa?
no. But you should show the documents from your arrest and evidence that the proceedings were terminated. If the embassy/consulate gives you a hard time, argue the petty offense exception.
The record does not make you inadmissable to the US, but the actions you took that led to your record may make you liable to be denied for any visa.
The Embassy will be quite curious as to what you were doing that day that you got arrested for shoplifting and burglary -- and they may not be as satisfied as you are with the decision to dismiss the case. You will need to do a good job of explaining your actions -- especially as they come across on the police report -- to gain a new visa to the US.