When Mr. Rodman visits the first time asking for a list of children, watch as he is in the buggy and leaves. The driver has trouble getting the buggy to move, the horse team is struggling. The driver suddenly realizes he forgot to turn the brake off.
As Murphy saves Emma, he wraps Emma to the front of him, having her wrap her legs around him. When the scene changes to the stuntman and stunt woman coming down the hill, Emma is now hanging on the back. Then at the bottom of the hill when it switches back to the real (non-stunt people) Murphy and Emma, she is again on the front.
Mr. Rodman makes a curious statement when he visits Gold Hill and asks for a list of the children. He says he and Ms. Tuttle will be staying in town a few days and to bring the list to the hotel. But in the episodes 'The Spy' and 'Eight-Eight Keys to Happiness', he goes to see his mother and it is insinuated he lives there too, and his son lives there after 'The Spy' episode. In Episode 7, False Blessings, Ms. Tuttle asks "...where are we going for lunch?" and Mr. Rodman answers "I am going home."
At the end of the 'Ghost of Gold Hill' episode, they receive the deed for Gold Hill. Surely someone as connected as Garrett would know they own Gold Hill (in other episodes he knows who owns properties), so how could the scam of needing to buying a building for a gambling hall work? They have gambling equipment already, as witnessed in the 'Eight-Eight Keys to Happiness' episode. Also, when Murphy gets the wire from the Bishop and tells Moses that the Bishop is turning the school over to the territory. But Murphy has the deed, not the church. The Church could turn the kids over however.
After saving Madeline, Murphy and Madeline come down toward the camera down the hill. You start seeing the kids on top pull the rope *up* the hill. Why wouldn't they untie it at the top and let it drop *down* the hill?
Early in the episode, we hear and see that Garrett is having his name added to signs around town, including the general store, hotel, and saloon. After Murphy fakes being drunk in Garrett's saloon and Garrett says he is going to make sure Murphy gets the building, there is a shot of a wagon going by Garrett's saloon and General Store. Notice the signs - now they are back to the old saloon sign and the Garrett name is not under the General Store sign. A little while later after the "wait for the wagon" song, there Garrett sign is under the General Store sign again. After the proposal, the Garrett sign under the General Store disappears again. After getting the papers signed, the old Saloon sign is back up. At the last scene after the wedding, the old Saloon sign is up.
Just prior to Murphy asking the shopkeeper about the addition to his sign, he waves goodbye to Father Parker. Notice there is no flagpole anywhere in sight. During closeups after that with the shopkeeper, there is a flagpole and flag right off his right shoulder. It is too close to be missed on the wide angle. Then when he pulls away there is no flag.
This curiosity occurs many times in the series. When Mr. Rodman shows up the first time, Father Parker is there. Murphy says, "Here we go again" and rushes up to the loft to put his priest uniform on. As long as there is a priest there, what does it matter? Father Parker goes off on trips. If Rodman asked about Father Murphy, they could just say he is off on a trip, visiting the Bishop, praying, etc. He just couldn't show his face in civilian clothes.