Frameworks like libgdx are great: you develop a game and deploy it for PC, Android smartphones and tablets, iPhone, iPad, html5 and ouya. Sounds perfect, doesn't it? But multi-platform development means more than just engine-side support: the game design is important, too.
A summary of some problems I encountered while developing Project S.P.H.E.R.E.:
Most platformers come out for consoles and / or PC. There are lots of endless runners for mobile devices as well, but "real" platformers seem to be rare. The main problem are the controls: platformers need fast reactions and intuitive controls for pixel-perfect jumps. That may work on keyboards and gamepads, but it's very difficult on touchscreens where you have no real feedback.
A possible solution is the Accelerometer. It's less precise than keyboard+mouse-bindings on the PC, but controlling the sphere with the Accelerometer works surprisingly good.
The screen size
It may be less important on tablets, but on smartphones the screen size can be a big problem: all the buttons, informations and views must fit the screen size. And, of course, you can't see what's behind you fingers when you touch the screen...
A mobile device is no PC. Especially "expensive" things like dynamic lighting could be laggy on lowend devices. Reducing the details and / or optimizing the code are often important. You can't see every detail on mobile devices, and sometings it gives a great performance boost e.g. when you slightly reduce the detail of lighting.
An unusual problem. When playing on a smartphone, e.g. while waiting for a train, you often play in brighter environments than a dark room inside a house (->on PC). The problem is that you can't see anything from the game if it is too dark. Finding a good balance between atmospheric darkness and eye-friendly lighting isn't easy.
I already mentioned the higher difficulty on mobile devices resulting from the different controls. Passages that can be done without any problems on PC can be hell with Accelerometer-controls. Again, a good balance between difficulty and playability is difficult. In some cases, slightly different levels between different versions can be useful.