I've had my first play few days ago and we were wondering if we're playing correctly. Does the final mission increase panic just as the normal ones do if not complete?

Also if I'm already playing four blue dices and have a card that lets me use another one, can I do that? There are no more physical dices but can I re-roll one?

As for the dice, you can use as many as your abilities allow. There is also mention in some part of the rules that your rolls are not limited by the amount of actual dice provided in the game.

For the Mission, I may be completely wrong, but I have never heard of a rule that would cause panic to increase if a mission was not completed in any given round. The only times panic should increase are if UFOs are left on the continent or card-effects or damage to your base.

UFOs left in orbit

UFOs left on continents

Crisis card effects

Damage to your base triggering the critical effect of the mission

Going under budget and having to extort funds from a country

Those are the only things I can think of that will raise a countries panic levels.

And yea, just re-roll as many blue dice as necessary.

Ufos in orbit dosent increase panic.

They do. For every UFO remaining in Orbit, the least panicked continent moves along one space on the panic-tracker.

If there is ever a tie, you get to choose.