Late as but add my two bob.

people putting a dummy back in your child's mouth (but you can see they just touched the bit that goes in their mouth and you know they didn't just wash their hands)
This is actually a big reason why I have always avoided the dummy where possible and severely limited it when not. My mum got one for my eldest sibling when he was young and she remembered he dropped it on the ground and she picked it up and it was filthy and she realised at that point they are germ harvesters and never used one again. I only ever used one overnight when the baby was that way inclined, that way it didnt travel far and there was minimal risk of it being exposed to anything truly nasty. I had some level of control over the germs so to speak.

offering your child food you don't want them to have
If I had some of their food on me I would say "Thats ok, I have their lunch" or "They prefer this". But if not then I would just outright say "Yeah sorry, s/he's a bit young for fast food, aye"

playfully teasing them in a way that they think is ok (no malice intended) but that you aren't ok with (eg playfully calling a chubby kid 'fatty' or something like that)
The easiest way to AVOID offending them is to be offended yourself! And usually you are anyway!

letting their older children touch a baby when they are sick etc
I am with Onyx. I nip that in the bud before it becomes an issue. If the older child looks sick from the outset I would ask if they are a bit sick, they don't look all that well and when it is confirmed I would add "Well we better be careful to make sure baby don't catch it then".

disciplining your child
Bit of a mixy matchy. I am fine with siblings and parents expecting a certain respect for their person, their home and their belongings and I am all for them letting my child know their place in that. However if anyone goes outside my discipline code then I really couldn't give a brass razoo if I offend them! For example; Chilly was lying across the arm of the sofa - which is a no no with us. A temporary boarder we had at the time decided to teach him a lesson by grabbing him by the ankle and dragging him off the sofa. I put him in his place mighty damn fast. A simple "You know you aren't allowed on the arms of the sofa, get off" would have sufficed.