In general, double standards only serve to further undermine equality in our society. That said, I'm willing to put up with most of them that favor women given what women have to put up with.

Using the example above, if my arm were in a sling I would fine with the abuse jokes not being serious, I'll take that one in trade. Because when I go to a job interview I merely have to put on my suit and dress properly. My wife has to know if she's interviewing with a man or woman. If it's a man, she has to show the slightest hint of cleavage to be taken seriously. If it's a woman, she has to do the opposite to be taken seriously. In today's world, she should be able to dress in business attire without having anyone concerned with her chest (men and women).

Now false accusations, that's a very serious issue that goes even beyond a double standard. Because some accusations are guilty until proven innocent such as child abuse/neglect/assault and rape. The problem is the justice system itself. There are serious flaws when the most typical defense over the years is to put the victim on trial as opposed to the accused. It's a very flaky system developed from years of under-reporting, intimidation, disbelief (going back to the concept of marital rape) and victim blaming. Even if the accuser is acquitted, they'll never really be innocent again in society.