First Time Jitters
Staying in the yard or storage area is a good check for dry camping. You may also want to go for a weekend at a local park (to check those things which use hookups), or even one an hour or two away (to try towing at highway speeds). In any case, try using everything you can, not only to ensure they work, but to find out how to work them and their quirks and limitations.
You don't really shower with a 6 gallon heater. It's more using the valve on the shower head to turn the water on to wet down, off while soaping/scrubbing and then on again to rinse. Not only are you draining the hot and fresh water tank, you are filling the gray water tank.
Like with your horse in the old days, make sure your trailer is taken care of before you consider yourself. Stretch out your power cord to ensure you have up to 35' of reach, and if not, consider an extention cord. Have the 2 other adapters so that you can tap into any of the 3 common electrical sockets (15, 30 and 50 amp). 10' and 25' of drinking water grade hose, along with extra seal washers and covers for the ends to keep out bugs and dirt. A pressure limiter and an inline water filter are good ideas, as is an assortment of fittings to ease connections (45 degree, 90 degree, Flex, 4' hose). 2 10' lengths of sewer hose or the equivalent, as well as all fittings to connect them to each other, the trailer and the variety of dump station fittings out there. A clear elbow is a good idea, so you can see what is happening with your dump. Disposable gloves for handling sewer components, and a spray bottle of disinfectant for leaks (yours and the people before you). 2 25' (or possibly 25' and 12') sections of TV coax, with a connector between them, and a piece of coax to connect to your TV, of course. If you don't have a coax input on your trailer, there is a flat connector available which threads through your window sill. Possibly some telephone cord.
If you will be staying at non-traditional places (like friend's houses) you will want to add in at least 50' more of 10 ga electrical extension cord and 50' more of water hose (the flat ones are good for this). Also a 'water thief' fitting to go over a non-threaded faucet.
Cram the highest amp/hour true deep cycle batteries you can into your space/weight limits, and carry some DISTILLED water for them. One of those automatic battery filler bottles would be nice. A box of baking soda would be handy for neutralizing spills and if you really want to be prepared, have an emergency eyewash. Keep in mind that often when the trailer is plugged into the truck, it is sucking off the truck battery as well, so unless you have some kind of battery isolation system to protect your truck starting battery, it is a good idea to unplug the trailer before extensively using it on batteries (like overnight).
Some way to level the trailer (if not built in). Those interlocking plastic blocks are a reasonable solution, and can be used under stabilizing jacks as well. Chocks or other ways of keeping the trailer from rolling once set up. I resisted the high cost of 'Snap-loc' pins for my landing legs, but many nights of trying to allign manual pins and greasy fingers convinced me to go with them. They cut the time to lower or raise the legs 75%, and the aggravation 95%. A king pin lock may prevent someone from 'accidentally' rolling off with your trailer. A lock on the release lever for your hitch will frustrate those good ole boys who think it is a hoot to watch the fun after releasing your hitch locking mechanism while you aren't looking.
Don't forget a lighter for the gas stove, a full load of propane, and some water in the holding tank. I carry about 1/3 tank when travelling and don't fill it up unless I'm leaving civiliation heading for dry camping, cause I don't like paying extra gas to transport water. Lots of flashlights and spare batteries (including for your smoke detector, etc). Rain gear and more coat than you think you'll need. Tool kit, cleaning rags and a battery powered tire inflator, as well as spare oil/fan belt, etc for the truck. Plenty of garbage bags (some places require all garbage be bagged).
12v and 120 volt fans, a ceramic heater and possibly a catalitic heater. A CO detector if you don't have one built in. Extra blankets. Have plenty of holding tank chemical and toilet paper. Paper towels, too. Make sure you have all the manuals for the trailer and its appliances. A good guide to trailer parks. Memberships to get discounts (AAA, Good Sam, Passport America, etc for park fees and Good Sam (Love's), Flying J, etc. for fuel) The exact height of your trailer posted right on the dashboard of your truck.
Well there is more, but the cat has already erased this once...
