One thing i see off the top is your last action ...
Platform on landed (platform is not moving)
In one tick you are asking it to start the "Land" animation" then immediately play the "Idle" animation
that's not going to play them back to back as you would hope they would.
You could add a sub event and put "on animation finished" action instead, then it will play one then the other.
Right now they are stepping on each other and you probably won't ever see it play the "land" animation
its also getting overwritten again when you use the "on any animation finished" -> player set "runloop" action earlier.
One way to setup an animation system like this is to create a 2 global variables such as "CurrentAnimationState" and "PreviousAnimationState"
Then create a series of scenarios that change the animation based on whatever your current and previous state of the player's animation was in.
eg: when the player is running (on key right), you set "CurrentAnimationState" to "Running" and "PreviousAnimationState" to "Idle"
Then create a "check" that says If CurrentAnimationState ="Running AND "PreviousAnimationState = "Idle" -> Play animation "StartRunningFromStop"
Next you would create another check (on key right released) that says "If CurrentAnimationState" = "Running" AND "no key is being pressed" -> Player "RunningtoStop" animation
Then create several of these "checks" for every possible combination of types of animations you want to have in your game.
Each variation will be separate actions which makes debugging and tweaking much easier (although you end up with a lot more events) But the tradeoff is much easier to visualize and wrap your head around in more complex games.
Basically right now you just have several platform movements all firing off at the same time stepping on each other.
If you post the .capx file in dropbox or a similar service and post it for us we can tweak the file and show you how to fix it.