I know fully automatic weapons cannot be possessed; What else?
When I lived there Class III was perfectly legal.
If I have a large-capacity magazine, do I need to get rid of it?
No. Continued possession of large-capacity magazines (able to accept more than 10 rounds) that you owned in California before January 1, 2000, is not prohibited. However as of January 1, 2000, it is illegal to buy, manufacture, import, keep for sale, expose for sale, give or lend any large-capacity magazine in California except by law enforcement agencies, California peace officers, or licensed dealers.
IMHO, it's more a case of 'who' than 'what'.
There is an extensive list of items that are considered “assault weapons”
http://oag.ca.gov/sites/all/files/pdfs/firearms/forms/awguide.pdf