Synonym for "dingbat" or "crazy person" or "nutbar". Usually used to signify someone who's crazy or incompetent, silly or dumb. "Ding-a-lings" are usually also "out to lunch." They can present an inconvenience.
That weird rabbit Mr. Whiskers is such a ding-a-ling, he is so weird and freaky and he should stop smelling his feet and collecting his belly button lint. Uggggggh!