There is one quest in Broken Valley that can wait until after getting the battle tower (rescuing some people in the quarry tower), as well as one on sentinel island (retrieving a book from a boat in a tree). All other open quests will fail, and most NPCs will be unavailable (presumably dead).
After you get the battle tower, there will only be a few high locations that you still have access to in Broken Valley (the top of Lovis' tower, the tower and top of the wall at the quarry, etc) and sentinel island. If there are any chests you want to get, do so first.
You 'drop' an item by destroying it.
You will be able to unlearn your skills (for a price) once you have the battle tower, so you can invest in the 'packed and ready' skill to increase the number of inventory slots (if you have any free skill points), and recover those skill points later when you have access to the chest in the battle tower.
Alternately, you will have runners after getting the battle tower who can retrieve any common plants or minerals you need for potions or enchantments. You can destroy or sell off any plants, minerals or ore that you have plenty of, or which you will not need to use right away (keep any malachite gems you have, but everything else can be replaced).
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