iPad Pro 9.7-inch model and Apple Pencil I just got both a few days ago, and I really love it! I've been using it to take handwritten notes in my Calculus 2 class, but I noticed something that worries me...

I'm not applying a lot of pressure on the screen when writing, but the Pencil sometimes causes the screen to do that "liquidy" thing... you know, when you press your screen really hard and the color gets blotchy? (Whatever it's called.)

I mean, is this supposed to happen? Is it detrimental to consistently do it?

Or, am I just paranoid with my new toy?
is this supposed to happen? 

With regular pressure of the hand against the screen, no it shouldn't. However, if the way you are writing -- the palm may be directing all pressure to one focused area which may cause this to happen. 

Is it detrimental to consistently do it?

Many sources on Google say it's common to see the distortion with pressure but none mention long term functionality issues. I would, however, take it to the Apple store if you have Apple care (or warranty) and get it confirmed by them because: 

One site - a user did mention that he got distortion and Apple replaced the iPad, and he didn't get distortion on the new one. (I highly doubt it'll vary with the different devices but its an option). 

Also make sure your hands are dry and cool. Heat, moisture, etc. are not good for any screen. 

am I just paranoid with my new toy?

Nope! Enjoy your new Apple Device!