I haven't really watched recently enough to be able to come up with a lot of examples. Part of it is just the amount of money they seem to have. Unless there's some oil wells on that place, cattle don't pay for mansions and helicopters and fleets of Dodge pickups with custom paint jobs on them. There may be one or two ranches in Montana that have a helicopter so maybe that's not so far fetched, but Costner is always bitching about money so it's sort of incongruent.
Also the amount of drama is just over the top. Ranchers aren't getting in gun fights every couple of weeks. It's TV though so that's to be expected.
The two biggest WTF moments for me were
1) In season 1 Costner and another guy are driving by and see a cow calving a quarter mile away and instantly say "She's in trouble!" and grab a calf puller and go sprinting across the pasture to her. The calf puller is a real tool and they are using it correctly, but you can't tell at a glance from that distance that a cow is in need of help calving. You would have to be able to at least get a close look and if the calf is oriented correctly you would probably wait an hour or two and see that she's not making progress on her own before you decided to intervene. When they get to her they say "He's breech" and immediately start pulling the calf. If the calf was breech, then pulling it would be the right thing to do, but it would be pretty unusual to be able to just sit on her head and pull the calf. I would take her to a head catch but at the very least you would have to snub her to a tree or something unless she was practically dead already. Then they proceed to pull the calf which comes out head first (aka not breech) and (the most hilarious part) it sprints away the second it hits the ground. Even the most vigorous calf will usually take 10 or 15 minutes to get on its feet and then it will be staggering around knock-kneed trying to find its mother's teat to suck. A calf that has had a difficult birth and especially one that's been pulled might take several hours to even get on its feet. It would take several days before it could run like the calf did on the show. On top of that, the calf they used is huge, probably 200+ lbs so it's probably a good 2-3 months old.
2) The part where the bad guys drop clover out of a plane and kill all the Dutton's steers. Cattle can eat clover and alfalfa obviously, but if they aren't accustomed to it and get out into a field of really green alfalfa, especially when it's wet, and they eat a lot of it, some of them might bloat up and some of the ones that bloat could wind up dying. That doesn't mean that dropping 100 lbs of clover out of an airplane on a herd of 300 steers will result in them all immediately dropping dead. It would have no effect whatsoever.
You can tell that they get some nuggets of information from someone who knows about ranching, but then they run with it and it becomes painfully obvious the writers have no idea WTF they're talking about.