Only a few days after I contacted them to report a problem with the browser search plugin, the Miami-Dade Public Library System (MDPLS) has come through with a fix via Sr. Systems Analyst/Programmer Jose J. Rivero.
If you go to the MDPLS Library Tools & Gadgets page, you'll find a repaired and working search plugin, as well as an IGoogle Catalog Gadget and a Windows Vista Library Catalog Gadget. The search plugin works in IE and FF, and offers search completion too. But if you had the broken version, be sure to delete the old version before you install the new one.
Thank you, Mr. Rivero!