Is it possible to permanently miss items?

In Bastion, some levels have items lying on the ground. Some of them merely provide NPC dialog, others are weapon upgrade materials, all of them give a small XP bonus.

The levels I've already cleared are marked with a red star on the map, and I can't revisit them.

If I clear a level without picking up all the items, are they lost forever, or would I be able to replay the level in this case? Can I miss out on weapon upgrades by not being thorough enough?

All items that you miss turn up in the Lost and Found item shop. The only penalty for missing them is that you have to buy them instead of getting them for free.

Not really, having a New Game+ save you from loosing any important item. If you don't get it the first time you can always get it in a new round.