Hello Brett and welcome to GoY. Moss can be composted as long as there is not a huge amount of it and most weeds can be composted. Avoid seed heads and avoid roots of stuff like couch grass and ground elder that will grow through anything. The nature of your question indicates that you are new to composting. As you get more experience you may try a 'hotter' compost system when the above may not be quite such a problem.

Celandine is a big no addition to the above - they, like ground elder and bind wind, can remain buried in compost for years. Burn them or put them in a tub with water, to drown/rot them down, creating a kind of raw green waste to your compost. But make sure it is fully rotted down before using.

I never compost weeds!! I have enough trouble getting rid of them without respreading them!! so to be safe Dont.

im with maggy on this one . better safe than sorry .