What do you call someone who is very good at dodging responsibility for his mistakes?
One relevant term that has been in vogue for several decades in politics is deniability, as in "We suspect that Governor X masterminded the highway on-ramp closures to punish Mayor Y for not endorsing him in the last election; but Governor X is insulated from involvement in the closure order by several layers of underlings, so from a legal perspective he still has strong deniability."
Another common idiomatic term (which Dan Bron and Hot Licks note in comments above) is Teflon, referring to the no-stick surface used on cookware and utensils to make them easy to clean. As rhetorician notes in a comment above, the term Teflon initially gained political prominence in connection with President Reagan, who seemed to retain his personal popularity even when his administration's policies came under fire and when various members of his administration got into legal trouble. Reagan's political adversaries sometimes called him "the Teflon President" because they couldn't make any of the fallout from these setbacks and scandals stick to him.
An even older expression of a similar notion is contained in the schoolyard taunt, "I'm rubber and you're glue; whatever you say bounces off me and sticks on you." The rubber kid thus evades the barbs and accusations that are flying about, while the glue kid soon wears a lead cloak of adhering calumnies. This, in a nutshell, is how our adult political process still works in the United States.