So, here are my thoughts and feelings on it:
Paralysis Mark - Will people still use this? Hex decks now have no means to try and walk through town square, limiting them to either booting to go somewhere (and then be called out), their own adjacent deeds, or Shadow Walk. With an immediate range, you might as well Puppet them. Also, how many tournaments have been won with Hexes recently?
Ivor XP - I can see the logic as to why, as Soul Cage allows some serious abuse, but much like Paralysis Mark, has this been causing a tournament winning deck? If not, is it weakening something that hasn't been winning anything, and thus doesn't deserve it?
Hot Lead Flyin' - There has been plenty of discussion about this card, and I imagine people expected something to be done about this. But was the addition of Headline as well as being based on the values of the dudes who actually are taken as casualties (meaning it can't be abused with casualty reduction any more), has the errata put this into a faux-banning?
Mugging & Nathan Shane - As they are not mechanical changes beyond an omission of the words "up to", I have no issues with either of these.
Gadgets - It makes sense for them to be able to use card effects to attach in non-controlled locations in the same way as non-gadgets, as having to boot the scientist to build it in the first place makes gadgets the weakest of the Hearts in my opinion. If someone used General Store or a similar card to have a discounted gadget at a location they don't control, I wouldn't have even realised that they shouldn't have been able to.
Weapon and Horses - I see it being in line with Tradin', as once you have finished trading goods you decide which horse/weapon you are keeping if you have more than one. I'm not sure how often you would attach a new Weapon or Horse and then get rid of the new one, unless you were playing them simply to get them out of your hand, but at least the option is there.
Sidekicks - Fixing an oversight where the new Sidekick spell couldn't be used for taking a casualty, the only thing that leaps out is they either won't make an action which attaches as a sidekick (much like Conditions attach), or if they do they will have to update this ruling again.
Send Home - No change, although on first reading the line "If any of these three effects cannot be done to a dude then that dude cannot be sent home booted." makes it seem like if a dude is booted, since you can't boot them again you then can't send them home booted. The wording could just be made tidier.
Instead/Replacement window - This would be clearer with a flowchart for me, to avoid any chance at misunderstanding, but I see it as Replacement trait > Replacement react > Responding trait > Reacting trait. If I have got that wrong, then it shows it isn't clear