You can watch the sphere if you ask Shinra. They unlock the door to the Den Of Woe and you will have to have all 10 crimso spheres to unlock it and here is where and when you get them;
No.1-Chapter 3:In Limbo(Under Bevelle where Vengagun was)before the Djose Temple mission.
No.2-Chapter 3:Received in Farplane Abyss from Nooj and Gippal.
No.3-Chapter 3:Same as No:2
No.4-Chapters 3 and 5:Chest in the Hidden Passageway in Leblanc's house.
No.5-Chapter 4:After the live concert talk to Leblanc in the engine room before talking to Shinra.
No.6-Chapter 5:Via Infinito(Bevelle).
No.7-Chapter 2:Received from Nooj in Ravine(outside of the Den of Woe).
No.8-Chapter 5:Via Infinito 20th Floor.
No.9-Chapter 1:In Ravine
No.10-Chapter 2:Examine the sphere in Ormi's room in the hidden passageway.
When you are in side the Den Of Woe there are no chests just lots of enemies and you will have to fight 5 bosses if you defeat them all you will get the book of magical dances 1 and the supreme light garment grid and your completed score will increase to a total of 6 times. The bosses you have to face are;
Rikku-HP7800
You will be Yuna and fighting on your own.
Paine-HP9200
Baralai-HP12220
Your team will be reunited now in this battle you can learn the attack Drill shot for the Gun Mage
Gippal-HP14800
In this battle you can learn the attack Mortar for the Gun Mage this is the only time you can learn this
Nooj-HP23800
And thats it.