The shapes that FT generates (especially the stringy ones and the fact that "mountains" are almost always centered on continents) are largely a consequence of it using a single fractal over the whole world. In http://www.fracterra.com/CGTutorial/ I recommended using the Wilbur Multifractal fractal type because it had fewer obvious implementation errors than the original one. These days I recommend using "RMF with Perlin's Improved Noise" because it has a wider dynamic range (it tops out around 26 octaves, where the Wilbur version starts showing artifacts at around 12 octaves).
One way to get more flat areas near the coast is to raise the continental shelf level closer to 0. Most folks don't care too much about underwater things and this is a way to trade one "realism" for another. Note that FT's climate model is very limited in that it doesn't take into account heat or moisture flows.
I may have broken the Expand land in offset feature in the last update. You can get a similar effect by selecting the land areas, expanding the selection, and then raising the land in that area. A smoothing step would probably help afterwards.
Remap altitudes is a direct port of the Wilbur tool of the same name. Due to the way that the fractal function beats against the editing tools, though, there is an unfortunate amount of roughness that appears (the same thing happens with the fill basins and set altitudes tools). It's most likely the roughness that you're seeing. You might be able to reduce that by doing a smoothing step after the basic operation.
One thing that you can do to tame FT's oddness is to find a world that you generally like and use the burn into surface operation. Then set the global roughness channel to something like 0.1 and you'll get a little fractal detail on top of the raw editing things. All of the artifacts in FT will be reduced by a factor of 10 in this case.
See the referenced tutorial at the top for a mild discussion of why deserts don't appear (short version: programmer picked bad defaults and used a bad climate model).
As mentioned above, FT has a static atmosphere model (no heat or moisture flow). This overly simplistic model means no wind or water currents, which in turn means nothing like rain shadow deserts. I know how to do it and machines are big enough now that it's workable in near real-time, but I still need to get around to implementing it.
The river flow finder has a hidden step that the incise flow tool doesn't: fill basins. If you can fill basins manually before incise flow as described in the link above, then the river results will likely be better.
Questions are good! I always like to hear from users of the program.