[Parody]

Since the statistics don't matter that much in Paranoia, converting adventures around is pretty easy. I tend to write a light framework for my adventures and then wing the rest as we go. For plot-important items, I come up with a summary of what role each NPC, R&D equipment, bot, or whatever has in that scene/the adventure/whatever, and go from there.

Something that may trip you up a bit is the changes in the backgrounds between versions. Between 1st/2nd and the later versions the Cold War aspects have been downplayed and you may find your players know nothing about what they were parodying in the first place. XP heavily plays up the Internet and capitalism, mostly in an attempt to make a campaignable version. 6th drops a lot of everything that doesn't fit on a card.

Speaking of cards, one thing I'm worried about in 6th (assuming you're using the cards) is that players will forget about anything they have that isn't represented by a card. I don't know if I want to make cards for, say, the various R&D devices I give my Troubleshooters in every adventure. Again, this is Paranoia and the rules are above the players' security clearance, so you can just drop the cards if you feel they aren't helpful.

Mongoose is rewriting Yellow Clearance Black Box Blues for 6th, so comparing their treatment of that vs. the original or XP/25th Anniversary versions should give you a good guideline for conversions.