In the original Batman comics, The Joker started out as a sadistic serial killer; in the first two years he was used he killed close to 30 people. Eventually the editors decided that allowing him to kill so many made Batman look bad ? and not just bad, but incompetent, for not being able to stop him. As a result, for the next twenty years the Joker became a laughing idiot who robbed banks, built wacky gadgets, and pulled harmless pranks. Then in the 1970s Dennis O'Neil revived the character and made him a psychotic murderer again, even more dangerous than he was before.
* They did and do have a point, admittedly. Batman's inability to permanently stop the Joker while simultaneously fighting gods and demons does make him and the Gotham legal system look bad. There's a thin line to walk.
o An even stronger example is Batman himself. In some early issues of Detective Comics Batman himself would shoot criminals to death on a regular basis, until DC editorial director Whit Ellsworth asked the writers to tone it down and make it kid-friendly. This sounds incredibly jarring to modern audiences because Thou Shalt Not Kill has been Batman's defining moral principle for so long, rendering this early facet of his character almost unbelievable.
o While the general summary is true, it's an overstatement to say that Batman would shoot and/or kill criminals "on a regular basis" in the early days. There were two instances of Batman killing with firearms in the early days - he shoots a vampire, and kills Hugo Strange's Monster Men with an aerial strafing run. Both fit categories where killing is arguably acceptable, even under a traditional heroic code against killing.