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.
I see you have an interesting usecase. You've also mentioned the presence of a corpus(which a really good plus). Let me relate a solution that I had sketched for extracting the crux from research papers. 

To make sense out of documents, you need triggers to tell(or train) the computer to look for these "triggers". You can approach this using a supervised learning algorithm with a simple implementation of a text classification problem at the most basic level. But this would need prior work, help from domain experts initially for discerning "triggers" from the textual data. There are tools to extract gists of sentences - for example, take noun phrases in a sentence, assign weights based on co-occurences and represent them as vectors. This is your training data. 
This can be a really good start to incorporating NLP into your domain.