Is there any way to destroy a weapon created by a spell? I've tried hitting it, casting magic missiles, casting dispel magic, remove magic, to no avail. Should I just keep running around in circles until the duration runs out?

-that's weird indeed. you're talking 'bout the jan-quest with the giths in the tavern, don't you? played this two times and destroyed the sword with magic missiles (from the staff of m.m.). any direct damage spells, specially the ones without a save like m.m. should work on this one
-perhaps it worth trying Otiluke's Resilient Sphere on it
-if you succeed don't forget to loot the sword for the Greenstone Amulet, a great item

Thanks. Yes, it was the giths. Dunno why my magic missile did nothing to the sword... :( I ran around the table until it was unsummoned.

SPOILER
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Killed Hidden, he didn't even fight back. 9k XP -- and why on earth would I leave a Mind Flayer be? Was he supposed to show up at a later stage?

Also, does Jan end up doing more regarding Lissa and Vaelag than just this quest? I'm not planning on keeping him around.

uumm, no and no. I assume you killed the hidden at your second meeting after he assures, that the girl will be o.k. and shows his ugly face. then NO he doesn't show up again, although he's somehow related to the mind-flayer dungeon beneath the city. I killed him also, just for being ugly.
second: NO Jan has no further quests regarding Lissa, though I thought he has after mentioning he will kill Vealag if he ever hears of him again. but he never...so kick him (but you'll miss a lot of funny talks)

I must have missed out on something during the quest. Never realized that character was a mindflayer. I just let him live and the quest turned out fine.

so blessed are the ones who have eyes to close them...amen ;)