The Heat is an unusual buddy-cop movie in that the odd couple cops are women-- it's also unusual in being very funny indeed, and has a plot that pretty clearly hangs together, though it does not particularly feature credibility.
Melissa McCarthy is the "Dirty Harry" cop, and, like Dirty Harry himself, she would last about 24 hours on any police force that wasn't in an odd-couple comedy and took seriously the laws about the civil rights of suspects and the regulations of any police force in a respectable town.
I checked with a policewoman in the lobby, and any time a police person draws a gun out of its holster, he or she had better be able to provide a good reason for it, not just say she wanted to threaten a witness with emasculation after bashing him with a telephone book (or whatever it was McCarthy had thrown from the doorway upon entering).
Threats of emasculation are regarded as duress in many police forces, and I'm not fully persuaded that McCarthy was just bluffing.
But if comedy is supposed to relieve us of our inhibitions, McCarthy certainly does that, and her victims are always deserving of ill treatment, even if she does go on gut instinct rather than intellectual analysis.
Sandra Bullock is the intellectual one, the good cop who prefers to follow procedures-- and she learns to respect McCarthy more, I'm afraid, than McCarthy learns to respect her.
Violence and language may offend some people, especially coming from sympathetic women. But after Bridesmaids, I don't even try to measure offensiveness in women's movies anymore. And The Heat made me laugh out loud-- and few movies do that.