Question: I want to use my AD&D 2E Monstrous Manual for monster stats. What pitfalls should I look out for?
Most of the above comments are solid and I agree completely.
With re: to monsters, I find that everything up to 1e is pretty straightforward to just port over, maybe keeping an eye on Morale for some of the monsters (I seemed to have noticed some creep). Don't be afraid to lower a monster's attack damage die or play with AC to bring it in line with where the players are. OSE does have some monsters in their rulebooks, so use those as a rough guide. Using 2e MM is fine as well, you again might want to adjust down as others have mentioned.
EDIT 2: I also simplify or remove abilities of some monsters, to keep aligned with how OSE and Basic DnD roll. Monsters over time have had a lot of abilities added to them, and many can be safely ignored, unless its the monster's key feature
The other thing generally I'd say is that OSE plays much slower than 5e, for example. And maybe its just our group, but we're not rushing through things at the table. Lots of discussion, more RP, but also less getting stuck on the character sheet for answers, lots of creative solutions to things in game. Don't worry if the game seems to "crawl", sometimes it will, particularly when being careful in dungeons, but then the action is fast and furious when it occurs.
Last thing is that OSE does have that undead level drain mechanic. I know that's fairly polarizing, and things that drain energy levels are not unheard of on random monster tables. Just something to consider (or avoid those undead until the party gets some levels under them).
Report back on how your games go!
*EDIT: after reading your write up, is the intention that the party will be in a position to slay the dragon after 9 months, or is that just a known fact of the realm? What happens if the wyrm wakes up and they're not ready? Does it attack again then go to sleep, or is the campaign over at that point? Just curious. Sounds like a fun campaign!