In Tropico 4, I accepted several objectives but then discovered that once you have five unaccomplished objectives, you can't accept any more. Is it possible to dismiss an objective, once accepted?
It is not possible, and for a good reason. Several assignments offer a bonus up-front (like money or free blue prints). If you could just take an unlimited number of assignments, you could gather all bonuses without even intending to actually work on them.
Instead, the game forces you to decide what you actually want to accomplish. It would be great to get 5000$ for exporting 300 cars, but right now you're really struggling just to not have your citizens starve - so don't accept it. Or do accept it, intentionally agreeing to be bound to the contract even if it will take a long time to fulfill, and potentially prevents you from accepting other tasks later.
In the campaign, 1 or 2 tasks are often fixed and mandatory, though sometimes you can decide when to start them. It may be wise to accept them later, when you're ready.
Despite all this, the fact that elections and rebel attacks are mandatory, too, is a design choice I would personally consider at least somewhat questionable.
This means that you can wind up having to decline interesting assignments later on because you still have the ones you accepted earlier stuck in your 'quest log'.
Especially irritating is that both rebel attacks and the election count as quests towards this total (and will be assigned whether you want to or not).