Lots of people have tried to trademark Bitcoin. The US law is pretty clear on this: first use defines who gets to TM something...thus, there's no need for (or ability for anyone to obtain) a US trademark.
First use requires actual use. I don't think what Gox did constitutes a use in commerce, as it did not identify the source of goods or services, but instead, was used as a generic term to refer to something they (as well as many others) were selling. I.e. to the extent a trademark registration followed by no subsequent use is an asset, it isn't worth much.
For other countries, it's (AFAIK) basically first horse across the regulatory finish line gets the TM, regardless of who has been using it (doesn't matter who was first, what they were using it for, how long they were using it, etc). Mark used his own funds to defensively trademark it and then (i guess) purposely never enforce it so as to make it essentially free to use (he's a French citizen, i think, so he did this in France). I don't know if that means no one can TM it there or it re-opens the door for someone else to TM it...but he was praised for doing this for the community at the time. If someone came to you and asked you for a few $k USD to TM "bitcoin" in your country to pre-empt squatters, would you be willing?
Actually, it generally creates a presumption that the "first horse" has dibs. That isn't necessarily conclusive.
I think the term Bitcoin was practically born genericized because of its uninterrupted use by the public at large without any attempts to enforce the "trademark" against others. As for whether I'd personally spend a few K to trademark Bitcoin, probably not. If I thought it would be useful, I'd approve of someone with an interest in the term doing it, at least if I knew they weren't going to use it maliciously, which I probably wouldn't.