You should probably refer to yourself using the non-perjorative
web programmer. When I hear web designer, it conjures up images of high school kids and MS FrontPage.
That distinction is important, because programming ability is the big thing I am looking for. Many web designers will tweak cut and paste code, without ever venturing forth from elementary CGI.pm. Nothing wrong with this, if it gets the job done. Just make sure it doesn't show up on your resume as a Senior Perl Programmer.
After a year of phone screens and interviews, I have in my arsenal a question that weeds out %90 of the web wannabe's:
What is a hash?
Answer that quickly, correctly, and well, and you skip ahead to the Lightning Round.
