To be honest, I don't think there is a way to brute-force into Mord's mansion.

Dim Door, Teleport and Teleport w/o Error are ruled out, because the mansion is an extradimensional space and those spells can't do interplanar travel.

Plane shift is ruled out two different ways:
1) the mansion is too small; you can't appear 5-500 miles off target and still be in the mansion (I haven't any idea where you would end up instead. Best not to find out, I think)

2) You need a tuning fork that's specific to the destination plane. Given that the mansion-plane only exists for 2 hours/level, good luck in figuring out the right tuning fork alloy in time to use it...

Astral Spell: The mansion doesn't appear to connect to the astral plane (unless it was cast there, of course). I'd say that it doesn't, eliminating this (I'd probably also block attempts to Astral Project out of the mansion for consistency).

Gate: this would seem to be capable of connecting to any plane, and so it could work. However, I can see 3 problems:
1) the spell does say that it connects to the plane that you name. Quick, what's the name of the plane of this particular Mord's mansion? (Mord's mansion created by Intrope on January 14th around 10:30 PM in the library with the candlestick? )

2) It also says that the planar ruler can refuse to allow the gate to open. I'd be inclined to count the Wizard as the 'planar ruler'.

3) It raises a really nasty implication: if you can use Gate to Extra-planar travel to Mord's mansion, could you also use the Mord's mansion as a source for summoning creatures? (Intrope, I choose you! ) Just to head this ugly line of thought off, I'd rule gate right out.

Ghost Form or Gaseous Form: the portal to the mansion is a dimensional portal, not a door. When it's closed, it just isn't there so I'd say these spells wouldn't work either.

Of course, this doesn't mean that there isn't any way in; subtlety would work though. Invisible creatures could sneak in when the portal's open; the same is true for incorporeal/gaseous beings. Disguises might work. Dopplegangers might be effective. Any shapeshifter might be able to pull it off. If all else fails, lying, hostage-taking, bribery, etc. might work.

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