For secrets that are not specific to The Silver Seed's added content see Serpent Isle's Secrets page.
Reach Furnace Early
While in DeathWatch Keep you may notice that the pillars in the banquet hall are duplicates of the Pillar of Fire in Furnace, a place that is originally visited much, much later in the game. Double-click one, pass the Test, and you'll end up in Furnace. You can then open the southern passages and return to the mainland. However you cannot use this exploit to enter Moonshade early as the door is locked. Despite being clearly not an intentional feature this exploit causes no plot disruptions (unless you count information you can get from the gargoyle earlier than intended), and the game can still be completed normally.
Once you've passed through a Serpent Gate to DeathWatch Keep it is possible to become a demigod! Simply find Surok the healer (his infirmary through a door north-east of the arrival platform) and kill him. Then go out and allow traps or enemies to kill you (but preferably not your party). Poison or even powder kegs might help here.
After dying for the very last time you'll awaken in the healer's quarters. You have now ascended to demigodhood! You will still take damage, but every time the final blow is dealt you regain 1 HP. Your party members, however, do not share in your supernatural blessing, and remain most decidedly mortal.
When running under Exult there is nothing more required, your immortal status will remain throughout the game. In the DOS original this status is seemingly fixed as soon as you go back through the Gate, but not if you exploit yet another oddity. The banquet hall's pillars are duplicates of those used to enter the Test of Virtue; simply double-click one to be taken there. You must pass the Test in order to open the southern drawbridge and return to the mainland (ask the gargoyle to lower it). Once again, this causes no plot disruptions.
Immortality can also be granted by enabling Flag 29 (si_tournament) via the cheat interface. This method also allows it to be enabled for characters other than the Avatar.