Never use # as your HREF; use a real link, and return false from your click event-handler. Also, if this is simply to power some GUI element, I highly recommend against using an A (anchor) tag, as anchor tags are meant for LINKS, not GUI controls. If you need a GUI control, use an input button (that's what they were made for!).
The selector $('.advancedOptionsPicker') would likely benefit from some context; e.g. something like $('select.advancedOptionsPicker') or $('.advancedOptionsPicker', '#optionsPickerContainer').
You might want to look into Document Fragments when constructing & appending lots of HTML manually.
