If these issues involve submissions to a particular conference, journal or grant they generally get resolved through the program committee chair, editor-in-chief or program officer. But often these problems go beyond a particular venue.
What if we had a TCS Ethics Board composed of a few of the most trusted members of our community? For example, if two people argue whether or not they proved the same result independently, the board could first try to come to a mutually acceptable resolution and if that fails, make an independent assessment that could be used by PC chairs and EiCs.
For more egregious cases of intentional plagiarism and/or theft of ideas, the board could write a stern letter that would go the perpetrator's supervisor and possibly recommend banning that person from publishing in various TCS journal and conferences for a specified period of time.
The vast majority of TCS researchers are quite honest and to a fault share credit for their ideas, but every now and then some researchers, probably not even realizing they are acting unethically, create an atmosphere of distrust with their actions. An ethics board would show that we care about proper academic behavior and giving a confidential forum where people can address their grievances and hopefully resolve issues before, as had happened, driving people out of our field.