Around 19 minutes in Lucien shoots a padlock off a container. As has been proven on Mythbusters, it's not possible to do that - regardless of how many times it's seen on TV and in movies.
When Longmire, Henry, and Cady are standing in Henry's office discussing the suspects in Longmire's wife's murder, Cady snags the mugshots from her dad's hands and stares at the first one. The next time we see the mugshot in her hand, it's a different guy, but we never see her flip to the next shot. However, if we listen closely we can hear papers shuffling so we can assume that Cady quickly changed sheets.
At one point, Longmire and Lucian Connolly are both wearing visitor badges, but it's spelled VISTOR on both of them.
At 07:26- when Walt says: "each one a little smarter and more ruthless than the next", that makes no sense. If he had said: "each one smarter and more ruthless than the last", that would make sense.