I realise that this is probably a really stupid question, but I will ask anyway since I can't really seem to find any information on it in the manual.

Once one person has claimed a public objective card, and therefore placed their marker upon the objective, can other players also qualify for that same objective later on in the game? Or is that objective exclusively taken?

No, anyone else can still claim the objective. The only restriction is that YOU can't claim the objective again.

(Don't worry about questions, I asked enough when I first started out!)

+1 to possum.

TI3 is an absolutely giant game, no one here would blame you for missing a few things. =)

For what it's worth, the only objectives that are only "claimable" by a single player are:

- Secret Objective: only the player dealt that objective can claim it

- "Special" Objectives (the green ones from the expansion): Only one player can claim them at a time; if another person gets control of it, the first person loses it (and the point).