What are components for

• Head over to GameStop to score an alternate costume for Serah.
• Amazon is offering an exclusive boss battle against Omega in the coliseum. After defeating him, you can enlist Omega as one of your allied monsters.
• Best Buy is giving away the Final Fantasy XIII Episodei novella

Source: Final Fantasy XIII-2 Pre-Order Bonuses Revealed

Edit: Amazon's also offering $20 credit.

As Yuck mentions in his answer on whether a new game plus mode exists, each area has an item that—once retrieved—lets you reset the area and play through the events again. This allows you to pick different Live Trigger options and get the reward you missed.

As an example, once you complete New Bodhum -003 AF-, the next stop is Bresha Ruins -005 AF-. There, you'll find a key item called the 'Leaving' Gate Seal, which allows you to close the New Bodhum -003 AF- gate. Closing a gate will reset the events of the area, and thus, allow you to get the reward.

Also of note is that closing a gate will unlock new Live Trigger choices, replacing some of the old ones. Based on the list in the strategy guide, most of the replacement choices are the "funny" options, so an efficient strategy would be to get the "serious" reward first, then get the "funny" reward once you can close the gate seal for the area.