that of the management. So give your coworkers some slack.
Human nature comprises "the good, the bad, and the ugly." For the "bad" to manifest itself, there's usually a "higher up" that'll condone or "legitimize" the bad behavior.
Try not to be in the mode of "me vs them." Treat others as equals, fellow human beings. Demonstrate that benefiting the team is your priority, not proving who is right.
In an office, try not to point out someone's mistake directly. Rather, say something like, hm, I'd take a closer look at this...