I mention below that I collect dictionaries and style guides.
I wish more copy editors did. We work with words every day. It stands to reason that knowing more about words (just knowing more words, for that matter) would make us better at our jobs.
Owning at least two dictionaries should be a requirement for a copy editor. You can't find everything you need in one. Webster's New World is often standard, as it's the Associated Press dictionary of choice. I don't care for it, but it highlights Americanisms. Merriam-Webster's Collegiate is very good (lots of words in a compact package). The American Heritage Dictionary was used at my college paper, and I'm fond of it too.
The actual dictionary brands don't matter as much as the frame of reference. The more information you have, the better choices you can make.