attorney made critical errors to my case, should i be charged for the lawyer's mistakes under CA professional rules

It is probably NOT ethical for the attorney to charge for this. You may find California State Bar Arbitration Advisory 98-03 of interest. It reads in part:
"In the context of litigation an attorney's negligent act or omission may be fatal to the case, i.e. the failure to timely file the complaint within the statute of limitations, or the failure to file opposition to a dispositive motion, resulting in summary judgment or dismissal. If the attorney's negligent conduct has caused damages to the client, the arbitrator is not permitted to award damages to the client or to allow an offset against fees for damages incurred by the client. However, if the negligent conduct has caused the loss of the client's entire claim(s), it is likely that the services were without value to the client. In cases where the attorney's error does not defeat the client's entire claim, the attorney may have billed the client for the cost of correcting his or her negligent conduct. An example of this might be the attorney's failure to timely respond to discovery, resulting in law and motion proceedings, or a waiver of objections which could have been asserted, and/or an award of sanctions. The attorney may have then diligently prosecuted corrective actions such as a motion for relief from waiver of objection, and billed the client for all of the corrective action costs. The arbitrator may not award damages or offset but may consider whether fees should be disallowed or reduced for services performed by the attorney to correct his or her own errors. The arbitrator may also consider whether the attorney's services which were negligent provided no value or lesser value than what was billed. The amount billed may be adjusted based upon whether the client received reasonable value if the services were ineffective or produced no benefit."
It is probably worth while calling this advisory to your lawyer's attention. The full Advisory is available without charge from the Califiornia Bar on it web site: http://calbar.ca.gov/state/calbar/calbar_home.jsp
Search for Advisory 98-03 and print it out for your use.
Be civil and reasonable, but firm in your talks with your lawyer.
You have the right to request State Bar fee arbitration with your lawyer if you cannot work things out.
Your lawyer knows this (or should) and will be reasonable if you approach this the right way.