Here's a quick tutorial that shows how to use the new door types with triggers to set up a level which has 'locations' -- areas that you can enter just once. When the two locations are completed, a third boss location is unlocked.
You can use the NOITEM trigger with regular items too; they don't have to be blue doors. For example, if you'd like a block to permanently appear after an apple has been collected, set the apple's COLLECT ONCE parameter to 1. Then group the apple and the block (select, shift-G) and set the block's trigger to NOITEM. If you'd like the block to permanently disappear along with the apple, do the same but set the trigger to GROUP.
For more complex examples, you can see a lot of these triggers used in Twisty Castle. For example, the four pots that you jump down are grouped with their respective blue doors and triggered with 'GROUP' so that they no longer appear after the section has been completed.
The doors system has changed in 0.2.10, but I haven't finished new documentation / tutorials for it yet. Instead of using the doors in the 'Items' tab, please use the user-defined ones in the 'Objects > Doors' tab.