In addition to horizons don't forget to pay attention to verticals when shooting buildings or structures. It's nearly impossible to get them right when shooting handheld in the park, but if your using light room take advantage of the guided upright feature to straighten everything up. This photo for example I straightened everything and that small thing makes a difference even if it's only slightly off. This is a little more extreme example as I had to point up, but illustrates it well.
Trash cans can be used as tripod substitutes and WDW has plenty of trash cans. Just keep a good eye on your camera! A small gorilla pod or small bean bag would give you more flexibility with your shot.
I've also used the top of fence posts for stabilization - but always keep my camera strap around my neck to prevent disaster from camera falling.
The biggest cause of a blurry or "unsharp" photo is too slow shutter speed. As a general rule, your shutter speed should be the same as your focal length. For example, if using a 50mm lens your shutter speed should be at least 1/50th of a second. For a 100mm lens it should be 1/100th of a second. This rule applies to a full frame sensored camera.
For a cropped sensor camera you need to multiply the full frame equivalent crop factor by the focal length. For example; in a APS-C cropped camera with a full frame equivalent of 1.5, a 50mm lens should require a shutter speed of 1/75th of a second (50 X 1.5). For a Micro 4/3rd camera the factor is 2X (50mm = 1/100th sec shutter speed).
Again, this is for general shooting. If you or the subject (or both) are moving you need to increase the shutter speed more.
For Dark Rides I generally look to shoot at 2X the focal length. The following shot was taken with at 55mm lens @ 1/100th of a second on a full frame camera (f/1.8, iso 6400).
Other factors that could effect this;
how you hold your camera is important. Feet shoulder width, camera close to body and elbows in will create a strong base to keep your camera from moving too much. I try (when I can remember) to press the shutter after I exhale.
Stabilization. Some lenses have stabilization and some camera have sensor stabilization. These are tools the help keep offset natural movements by the photographer. They can generally allow a slower shutter speed, but work best when the subject is not moving. It is not a substitute for holding your camera properly.
When shooting sports or other fast moving objects, shutter speeds have to be much faster if you want to freeze the action. Generally 1/800th or faster.
If you're not the camera warrior type with a robust bag and a weatherproof camera... Stash a gallon-sized ZipLoc bag (or two) somwhere. If there's one of those infamous Florida downpours at 4pm, you can stash your camera (and cellphone) in them for the duration. Also good for rides like Kali or Splash.
Want to save some space? Most chargers, including those from your camera and MacBooks can take one of these. This lets you pack less stuff, cutting down on weight/bulk. I know for both my Leica and Fujifilm chargers, this plug saves me from having to pack the supplied A/C end; which is a 6' cord. I also use it for the MacBook Pro charger. I have one for 220v as well, for traveling overseas... Most chargers are 110/220v and require nothing more than a different plug. Click:
Be careful packing too much gear in your shoulder/messenger bag. It's one thing to bring everything you want back/forth to WDW - but leave stuff you know you won't use in the room's safe. For example; I occasionally bring a long zoom - which I only use at AK. Unless I'm going there that day, I don't bring it. A heavy bag will cause you loads of grief after a few hours.
Similarly, forget camera backpacks. I know a lot of people like them... And they're great for getting gear from A to B. But to shoot out of them is a PITA. You have to take it off your back, swap lenses, then put it back on. Instead, consider a sling bag. It's a cross between a shoulder bag and a backpack, with advantages of both. Just keep in mind how open the side(s) is; one that only lets you stash your camera quickly (or opens on the back) is not really conducive to lens changes.
When choosing lenses to bring... I know, the agony of the decision, right? You're on vacation - not a photo shoot (like I should talk). Bring two (or three) zooms to cover a wide range and one fast prime lens (like a 28-50mm f/1.2-1.8) for the evenings. If you happen to stop at the room in the late afternoon or evening, you can even swap them... And enjoy the freedom of just a camera with a prime at night. Don't forget a small flash for fill light.