The problem for me was solved using Chrome. Firefox on both Mac and Windows — probably something to do with a plugin (NoScript?) — wouldn’t let me add any Tags into posts, or add new Categories. Tried it again with Chrome, and worked like a charm.
Symptom for me was that the tag box kept the default “Add New Tag” value, even when typing in something else. That gets cleared automatically in Chrome when typing. So, seems to be a javascript-type issue.
Hope that might help someone.