To unlock the safe in the Shinra Mansion, enter the corrsponding combination:
Right 36 Left 10 Right 59 Right 97
Going past any number whilst entering the combination will result in the code failing, for example when moving towards Right 59, going past it to 60 by accident (even without selecting it) and then going back to 59 will prevent you from opening the safe.
A boss fight will occur once you have opened the safe. For a good strategy in defeating this Lost Number boss, check out my Boss Guide in the Walkthrough section.
Advice on Cloud, Barret and Vincent's ultimate weapons
Added 31 Jan 2009, ID #13624
Cloud's Ultima Weapon decreases in power the more health he loses. If you want his Ultima Weapon to pack an extremely powerful punch, you should keep him healed. A fully healed Cloud performing Omnislash with his Ultima Weapon will cause a cumulitive amount of damage, even more damage than the Knights of the Round summon.
Barret's Missing Score increases in power the more materia you load it with. This is quite an odd combination, as Barret should mainly be used as a physical attacker, but you'll cause a greater amount of damage the more materia he has in his Missing Score. Perhaps it's one of Squaresoft's tricks to catch you out. Barret performing Catastrophe (level 4 limit break) with his Missing Score overloaded with materia causes an immense amount damage to opponents, and is up to par or near-par with Cloud's Omnislash and Cid's Highwind.
Vincent's Death Penatly deals damage determined by Vincent's kills multiplied by five. For example, if Vincent has killed 200 enemies throughout the course of the game, the damage dealt by his Death penalty will be 1000 HP, no matter who or what the enemy is, unless they use Barrier/Wall. A good way to boost Vincent's kill count is to give Vincent the Slash-All materia, and head to an area where you can encounter groups of five enemies, such as the Mythril Mines or the forest area outside of Junon.