If a person in custody of law enforcement began to harm themselves, like how the guy in one of the jail cells was scratching the walls with his fingers until they bled, or the other guy who kept banging his head into the bars making his head bleed, the police officers would not just allow them to continue hurting themselves. Procedure dictates that a person intent on harming themselves be put in restraints so that they cannot do so.
During the flashback of Dean holding the First Blade, he gripped the table with his left hand as if he was holding the blade but he should have used his right hand because he has the Mark of Cain on his right arm.