Here's what I learned, in the corporate world; if it's the same in the ED as in an office, this holds true. The company I used to work for had, I think, a very reasonable policy: people could date, as long as they weren't in a boss/employee relationship themselves, and didn't both have the same boss.
The problem with dating within a department isn't the reality, it's the perception. And that's what kills it; there's no way to prove a negative in a lot of these situations. Everyone involved is an adult, and we're all professionals... but that doesn't end the discussion, and it doesn't prevent the hurt feelings and the gossip and the lingering resentments.
The Sr. Resident is in charge of the schedule? And oh gee, see how her boyfriend the PGY-2 just happens to have Memorial Day Weekend off... hmm.
It can be completely innocent and unrelated to the relationship, but there's always somebody who will see a connection. Sometimes it's everybody. The alternative is to treat your significant other WORSE as an emplyee than you would if you weren't dating, but that's not so fun either.
In general, it turns out to be either flat-out not worth it, or certainly a minefield. I've done dumber stuff for love, to be sure. It's just that I'd recommend the parties involved think twice about it, and then think a little more.