do i have a case to sue this nursing home

Your father may be the victim of neglect which is considered a form of abuse under the laws which govern skill nursing facilities. The Department of Health Case Services has published an informative pamphlet which may be found at http://www.cdph.ca.gov/HealthInfo/Documents/AbuseWhatToDo.pdf. If you suspect your father was the victim of abuse, you may file a complaint with the Department's District Office for the district where your father resides. The telephone numbers are listed on the second page of the pamphlet.
You may also wish to consult with an attorney to discuss the particulars of the matter and for specific legal advice about the possibility of a civil action.

Your description sounds like "neglect". It is usually a good idea to file a complaint with the DHS which will then investigate the claims. This will help uncover additional facts which you may not be aware of. You should also request a complete set of your father's records from the SNF. These should then be referred by a lawyer who does Elder Abuse cases. Keep in mind the statute of limitations can run as short as one year from the date of the injuries for some causes of action related to the neglect, such as simple negligence. Therefore, you should contact a lawyer as soon as possible.