Build text complexity model based on complex examples
There have been many ways to measure text complexity proposed in the literature, I don't have any particular survey to recommend but google is your friend.

Many of these measures are heuristics, i.e. they work in an unsupervised way. I don't remember the details but I've seen some works using a combination of several of these measures to obtain more accurate results. 

A basic way would be to be build a language model on the complex text, measure the complexity against this model for any new text and assume that if it's not similar then it's not complex, but as you rightly noticed it's not a very safe assumption.

At the most basic level, you can use the type token ratio (TTR): divide the number of types (unique tokens) by the total number of tokens. The TTR is a quite good indicator of lexical diversity, so complex text is likely to give a high value. It's a very crude measure but it's useful as a baseline: whatever system you try, if it doesn't give better results than a threshold on the TTR then it's not a good system :)