We got our TM last October and started picking up several (mostly convenience rather than necessity) items over the course of the first few trips.
Off the top of my head:
A lighter for lighting the oven/campfires. Firewood, and S'More supplies if you're going to have campfires
Grill for the campground fire pit, charcoal for CG BBQ and/or your own small BBQ.
Tablecloth for the campground tables
Small kitchen trash bags (we also have a foldable fabric trash can from Wal-Mart)
Can/bottle opener
Gridle/saucepan
If the TM has a vinyl floor, a broom (Wal-Mart sells an RV broom/dustpan that folds down to a compact size that will fit in the storage slot on the door.)
We also like to take an extendable squeegee/brush to clean/dry the roof of the rear shell before bringing down the front shell when we take it down.
Flashlight with spare batteries.
Some spare fuses for the Trailmanor.
Leveling blocks in case you end up in a site that is not level.
A small torpedo level if the previous owner didn't attach levels to the frame.
If you're taking a TV and using the campground cable, a couple of lengths of coax cable (1 short for inside, one longer for outside).
A door mat and/or larger outdoor mat.
Outdoor folding chairs.
A Laundry bag for the dirty clothes.
If you'll have AC power and it will be cool at night, a small electric heater. It's much quieter than the built-in furnance and you'll save on the propane (top off the propane tanks before you go).
For comfort we got memory foam mattress toppers from Wal-Mart for the beds and we use sleeping bags rather than bed-sheets - I sleep better in the TM than I do at home
RV or other toilet paper that breaks down fast.
Make sure you have or get a pressure regulator for the fresh water hose and a sealed fitting for the campground end of the sewer hose. You may also want to get an RV water filter.
As mentioned, there's really only a few essential items...the most important is a sense of adventure and a camera to document your experience. Have fun!