Question: I have a corpus of a few 100-thousand legal documents (mostly from the European Union) – laws, commentary, court documents etc. I am trying to algorithmically make some sense of them.

I have modeled the known relationships (temporal, this-changes-that, etc). But on the single-document level, I wish I had better tools to allow fast comprehension. I am open for ideas, but here's a more specific question:

For example: are there NLP methods to determine the relevant/controversial parts of documents as opposed to boilerplate? The recently leaked TTIP papers are thousands of pages with data tables, but one sentence somewhere in there may destroy an industry.

I played around with google's new `Parsey McParface`, and other NLP solutions in the past, but while they work impressively well, I am not sure how good they are at isolating meaning.

Answer: 
In order to make sense out of documents you need to perform some sort of semantic analysis. You have two main possibilities with their exemples:

Use Frame Semantics:
<http://www.cs.cmu.edu/~ark/SEMAFOR/>

Use Semantic Role Labeling (SRL):
<http://cogcomp.org/page/demo_view/srl>

Once you are able to extract information from the documents then you may apply some post-processing to determine which information is relevant. Finding which information is relevant is task related and I don't think you can find a generic tool that extracts "the relevant" information.
Don't use triggers. What you need is a word sense disambiguation and domain adaptation. You want to make sense of is in the documents i.e understand the semantics to figure out the meaning. You can build a legal ontology of terms in skos or json-ld format represent it ontologically in a knowledge graph and use it with dependency parsing like tensorflow/parseymcparseface. Or, you can stream your documents in using a kappa based architecture - something like kafka-flink-elasticsearch with added intermediate NLP layers using CoreNLP/Tensorflow/UIMA, cache your indexing setup between flink and elasticsearch using redis to speed up the process. To understand relevancy you can apply specific cases from boosting in your search. Furthermore, apply sentiment analysis to work out intents and truthness. Your use case is one of an information extraction, summarization, and semantic web/linked data. As EU has a different legal system you would need to generalize first on what is really a legal document then narrow it down to specific legal concepts as they relate to a topic or region. You could also use here topic modelling techniques from LDA or Word2Vec/Sense2Vec. Also, Lemon might also help from converting lexical to semantics and semantics to lexical i.e NLP->ontology ->ontology->NLP. Essentially, feed the clustering into your classification of a named entity recognition. You can also use the clustering to assist you in building out the ontology or seeing what word vectors are in a document or set of documents using cosine similarity. But, in order to do all that it be best to visualize the word sparsity of your documents. Something like commonsense reasoning + deep learning might help in your case as well.