Here's how I'm thinking of handling it, as I mull the CT rules
I'm trying, as much as possible, to extrapolate from the rules already built in to Books 1-3 when tweaking the rules. (I find the free-wheeling spirit for Throw resolution introduces in later adventures and in The Traveller Book to be a little too freewheeling. I re-read Shadows the other day and found the Throws to be so scattered in the logic that after a while they just seemed arbitrary.)
To that end, I'd use the STRENGTH and DEXTERITY modifiers for weapons found in Book 1. Eyeballing the tables, the bonus kick in at a characteristic of 8 and are awarded up to 11 or 12.
I don't want anything too complicated. (I'm drawn, to, for example, Mike simple binary of Throw 8+ for basic at-risk situations and 12+ for tricky at-risk situations. (I say at risk, because I can't imagine rolling if there isn't some sort of conflict with another character or something on the line where failure will be interesting.)
In the spirit of keeping it simple, then, it would go like this:
1) The Player notes that he thinks his Characteristic would apply in the given situation.
2) If the Characteristic is 9-10 he gets a +1DM on the roll. If it is 11+ it is a +2DM.
3) If a pertinent Characteristic is 4-, then there is a -1DM applied.
[These bonuses and penalties do not apply to situations using weapons or combat. The rules already in place handle those.]
Note that this encourages Players with PCs on the breakpoints, if they think it's worth it, to use the Experience rules to bump up their Character's Characteristic using the Experience rules.
There is one other rule I'd be thinking about using, when Characters are in conflict with each other:
1) If one character has a pertinent Characteristic value 2x the value of the opposition's pertinent Characteristic value, the character gets a +1.
So, if someone is bossing a manservant around while trying to get into a private home, and he has a Social Standing value of twice the manservant, there's a +1DM for the role.
That's how I would use Characteristics. They are never assumed to apply, they have to be justified in how they apply, and they apply a slight bonus or penalty when above average or distinctly below average.
EDITED to follow up on Mike's post:
I, too, would award +1DMs as Mike awards them:
+1DM for roleplaying the event well.
+1DM if they have a specialist 'tool for the job'
I would also provide DMs based on Skill. Usually 1 per level, other times a DM multiplier for highly specialized skills, to allow a guy trained in Vacc Suit or Engineering to shine in a difficult situation. As a Ref I would talk this through with the Player(s) -- really getting a feel for how difficult the situation is and how getting a solid description of how the skill is helping. If it makes sense that the skill multiplier should apply, it applies.
As much as possible, for Traveller, I want the Players really touching and manipulating the world to describe how they're going to do things or solve problems in interesting ways. And I want to reward them for doing so.