Section 922(g)(1) prohibits firearm possession by any person “who has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year.”
The definitions for the terms used in § 922 are set forth in 18 U.S.C. § 921. 18 U.S.C. § 921(a)(20)(B) defines the term “crime punishable by imprisonment for a term exceeding one year” as not including “any State offense classified by the laws of the State as a misdemeanor and punishable by a term of imprisonment of two years or less.”
The above is straight from the Justice MTD (and the quotes are straight from the statutes - I double checked).
So besides a Misdemeanor Conviction for Domestic Violence (of any kind), as the law currently stands any federal conviction of a misdemeanor that could have led to a sentence of more than one year, or a State misdemeanor conviction where the sentence may be more than 2 years, disqualifies anyone from possessing firearms (or ammunition).
Now add to that mix, there may be individual State prohibitions on who are prohibited persons (and for how long). CA has a long list of convictions that would result in you being a prohibited person (varies by conviction from 5 to 10 years, IIRC).
Any such prohibition would not be approved for a CCW.