Hello - I am a new member to the game and this is my first post.

Why do some quests in the log window have check marks in them? It doesn't seem to be anything to do with completion and I can't select/de-select (as if to make it an active quest a la GW)

Completed refers to you having all items, or locating dungeons. It means you can now turn it in to whoever you need to see for the reward. With a quest that you only need to find that person all criteria for completion is already done when you receive it.

I have seen one quest show up in the log as completed when in fact it wasn't. I believe that it may be a bug, but whether it applies to all quests or just the one I spotted I can't say.

The quest that did it for me was the one from Ratsputin's holding cell where a woman asks you to collect X number of ingredients. Upon gathering these & returning to her she creates an awful beverage that you are then supposed to deliver to one of the Decemberists on the first level (I think).
After she'd given me the drink to deliver, but before I delivered the drink the quest was marked completed. It seemed to happen after I completed a completely different quest that wasn't marked off (can't remember which now).

Even though the quest was marked as done, the woman did not show that it was done & I could not talk to her at all. It was like she was visible but not actually there.

I eventually did finish the quest to deliver the drink & everything sorted itself out. Now I'm gathering Monster turds for her next concoction!

I think this may be what the original poster is talking about. I have only experienced this the one time (so far) & thought that it must have been that specific quest.
Maybe it's not an isolated incident?

It was marked as completed because the next leg of the quest, to take the drink to someone, was completed in the sense that you have the drink. There are several other quests that work the same way (the fizz potion quest comes to mind).

I don't believe that is quite how it worked. The quest was the actual delivery, not the gathering of ingredients or getting the drink.

The quest was not marked as completed after receiving the quest (which would confirm what you are saying), but sometime between getting the quest & finishing it.
After receiving the quest the woman's "!/?" was greyed out above her head as per usual & remained so the next few time I returned to knock off the farmer quests.
Once the quest was marked as completed in the log she had nothing above her head, greyed out or otherwise & would not talk at all, not even to give you the clap trap she does before she even has quests.

I only discovered that something was wrong after completing a different quest & finding that it was not checked off, but the womans quest now was. Unfortunately I can't remember which quest that was though.
If it was how you are saying, surely all this would have happened immediately after receiving the delivery quest?

I should point out that I after receiving the delivery quest I continued through the rest of the dungeons on that level over a few days before returning to level one to deliver the drink. When I got to the decemberist he also had no "!/?" above his head, but did interact with me to finish the quest.

After hacking & slashing your way to level 87 as a fighter the whole way, you do get to know when things are not behaving as they should & this was definitely one of those times.

It seemed that the first few quests I did had checks on them even though I was still collecting stuff for them - But I could have been wrong. After all of your explanations on how it works I looked over the quest I had and sure enough any that were checked were only requiring me to deliver something or to visit someone. It was just confusing when the log said I had completed a quest to see someone in Townston when I hadn't even been to Townston yet. It is just a little different than most MMOs I have played. For instance, In GW when you get that type of quest the log doesn't say completed until you talk to the person. Then you get a message and a sound that you have completed a quest.
Thanks for the info all...........