For a monk, how should the points be best distributed to the Thieving abilities. Should I max out on Find Traps, Hide in Shadows, Move Silently, or a combination.

Any difference if soloing?

IIRC, a monk is only able to locate traps, not disable them. Might influence your decision...

Finding traps comes without disarming them. The "Stealth Mode" comes without backstabbing multifier.
IMHO both qualities aren't great at all. I never used them. The monk is powerful and versatile enough without these "gimmicks".

Ugaya is right - the monks other abilities outweigh his "thief-like" abilities. However, I would probably dump points in hide in shadows first, follow that with move silently and then detect traps. I did use the detect traps a fair bit as a backup.

If you SOLO a monk, then definitely reverse the priority and dump as much as possible into find traps - you won't be able to disarm them but you CAN avoid them and that is half the battle!

By the way, I noticed that there appears to be an error in two of the monks special abilties: the Whirlwind and Greater Whirlwind attacks documented in the manual only give 5 (!) attacks per round / not the 10 listed! Its still an awesome special but just not quite as good as you would think.

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Whirlwind and Greater Whirlwind does set your attacks to 10 per round.