In order to be eligible to receive unemployment benefits, you must be available to accept work for which you are qualified to perform. It can be very risky for you to be particular about the job. If a job is offered to you, for which you are qualified and you reject it, without a very good reason for doing so, you run the risk of being disqualified for benefits. More problematic, if the EDD finds out, after you have been receiving benefits for awhile, that you have been rejecting job offers you do not like, the agency may demand you repay the benefits you have been receiving. Of course, if your work experience, skills and education are more in line with an executive position, you would not be expected to be a dishwasher. But if you turn down a job simply because you are apprehensive about a particular aspect of it but are otherwise qualified, you could have a problem. The way the EDD views it, it is better to be working than to be receiving unemployment benefits.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
Unemployment benefits are not intended to subsidize a claimant's search for the ideal or perfect job. They are intended as a temporary safety net for individuals who find themselves unemployed "through no fault of their own."
If you turn down an offer of "suitable work," then you will likely forfeit your right to collect UI benefits. See here for a discussion of what qualifies as suitable work: http://www.edd.ca.gov/uibdg/Suitable_Work_SW_5.htm#Elements%20of%20Suitable%20Work
Good luck in your job hunt.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents.