**Yes, each item found in the Sinnoh Underground have different rarities**. Some depend on your Trainer ID No. or whether or not you have obtained the Nat. Dex. Here's a List:
Spheres
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***Small Blue Sphere:*** Common
***Large Blue Sphere:*** Common
***Small Green Sphere***: Common
***Large Green Sphere:*** Common
***Small Pale Sphere:*** Uncommon
***Large Pale Sphere:*** Uncommon
***Small Prism Sphere:*** Uncommon
***Large Prism Sphere:*** Uncommon
***Small Red Sphere:*** Common
***Large Red Sphere:*** Common
Fossils
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***Armor Fossil:*** Uncommon, if trainer ID is even in number.
***Claw Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Dome Fossil:*** Rare (After Nat. Dex).
***Helix Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Old Amber:*** Rare (After Nat. Dex), Found rotated by 90 degrees.
***Root Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Skull Fossil:*** Uncommon, if trainer ID is odd in number.
Plates
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***Draco Plate:*** Very Rare
***Dread Plate:*** Very Rare
***Earth Plate:*** Very Rare
***Fist Plate:*** Very Rare
***Flame Plate:*** Very Rare
***Icicle Plate:*** Very Rare
***Insect Plate:*** Very Rare
***Iron Plate:*** Very Rare
***Meadow Plate:*** Very Rare
***Mind Plate:*** Very Rare
***Sky Plate:*** Very Rare
***Splash Plate:*** Very Rare
***Spooky Plate:*** Very Rare
***Stone Plate:*** Very Rare
***Toxic Plate:*** Very Rare
***Zap Plate:*** Very Rare
Additional Items
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***Blue Shard:*** Uncommon
***Damp Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Everstone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Fire Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Green Shard:*** Uncommon
***Hard Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Heart Scale:*** Uncommon
***Heat Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Icy Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Iron Ball:*** Very Rare
***Leaf Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex), Found Rotated by 90 degrees.
***Light Clay:*** Very Rare
***Max Revive:*** Very Rare
***Moon Stone:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex), Found Rotated by 90 degrees.
***Odd KeyStone:*** Very Rare
***Oval Stone:*** Rare
***Rare Bone:*** Very Rare, Found rotated by 90 degrees.
***Red Shard:*** Uncommon
***Revive:*** Very Rare
***Smooth Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Sun Stone:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Thunder Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Water Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Yellow Shard:*** Uncommon
> Sources: Serebii, PsyPokes, Experience.