"Account already logged on"
It happens to me too...no biggy. Hitting 'log on' a second time gets me in. This usually happens when I switch toons, but can happen when you first get on. I think the previous logout process gets 'hung up' and the second try completes it. I think it is just a techy issue, but there wouldn't be any harm in reporting it if you wish.

Seconded, I have it happen occasionally too, and have friends who've talked about it.
Generally nothing to worry about unless it happens constantly and/or you see suspicious activity on your characters(like being deleted, and the things you listed)
This is especially likely if you crash out of the the game and just decide to quit for the night, your character won't get logged properly from a crash alot of the time.
Both times I've signed into the game over the last two days I've been told my account was already logged on; a second attempt at signing in was successful both times. I dismissed it as an odd fluke the first time, but now I'm a bit concerned.
I've never shared my account or password with another person, so no one else has access to it. I don't see any indication of mischief (no characters deleted, no inventory missing) and none of my characters give any indication of being played (most of them haven't been logged into for more than 1 day; my currently played character was in the same location I left him).
I've changed my password as a precaution, but should I report this? Is this possibly just a technical issue?
Kid Lazarus, 50 empath Defender
Freek, 50 mind/psi Dominator
Black Khopesh, 43 db/wp Scrapper
Circuit-Boy, 40 elec Brute
Graf von Eisenfaust, 38 db/wp Brute
Blue Banshee, 35 sonic Blaster
Blood Countess, 33 mind/storm Controller
Dr. Radon, 32 rad Corruptor
Phantom Pirate, 32 db/wp Stalker