You don't say what you have for a fifth wheel. If you have a kitchen at the rear, things can bounce more inside the cabinets, and things can bounce out of the sink. But it depends on your particular unit, length, weight, axle rating, etc. and even the rating of the truck (1/2, 3/4 or 1 ton). Having a set of good HD shocks on the TV can help. If your kitchen is closer to being over the axles, you probably won't haven any problems. Generally speaking, in terms of physics, things closer to the tail end of a trailer will experience more bounce.
With our current TT with rear kitchen, things bounce out of the sink, cab. doors can open and even the grate has bounced off the stove. We have used a bungy cord on the door handles now. We've even had the vertical plastic rod for opening/closing the blinds on the rear window bounce off the little hook on the track. On our old TT with a kitchen over the axles, we had zero problems with anything bouncing out. Even the cutting board stayed in place on the counter.
With the TV, if you have a newer trailer, the TVs are quite light now. And if it was installed by the factory, it should have some sort of locking mount. If this is the case, you will not have problems leaving it in place. If you've added it, it depends on how you mounted it and the weight of it. An articulating arm mount can be heavy so along with the weight of the TV, if you have not secured the mount to something solid (like framing or joists) you *could* have a problem. I added a TV and articulating mount to the side of a cabinet in our old TT and I added bracing up to the ceiling joists. A factory often includes provisions for adding a 2nd TV and there will be a backing plate inside the wall. If you've added the TV, or are still concerned, you can add Velcro straps and use these clips: http://http://www.theclip.com/store/...cat=248&page=1
It'd be a nuisance taking the TV down all the time and you don't have to if you secure it with Velcro straps. I've even seen a few trailers come that way from the factory. But don't rely on screwing into thin luan plywood to secure anything. I'd consider Oscar rivets for that.
You won't know what bounce is like until you just go and use your FW. Most folks don't have problems while a few do. I've even read about some having clothes hangers jump off the rods in a closet. If you seem to have more bounce than you'd like, you could consider adding shock absorbers.
You should have no problems leaving loose items sitting on the floor. We leave cases of bottled water, a cooler, etc. on the floor and they're fine. For long distance travelling, you could always secure an item to a table leg or something with a strap or bungy cord.
If you ever added a rack on the back, that's where things can be thrown harder up and down because of the leverage effect. I read the other day where a guy had his bike thrown clear off but still stayed attached because of a cord attached to the rack. He dragged it way down the road before someone honked at him.
Otherwise, sometimes it's a case of just slowing down over potholes and bumps. A speed bump can end up catapulting things in the air inside your trailer if you hit the speed bump fast enough. I've done that a couple of times at the Canada/US border crossing.