There have been several Reddit threads and bitcointalk forum posts the past couple days regarding integrating a Turing-complete programming language with a cryptoledger.  Bitcoin currently uses a limited, non-TC language called Script.  The comments, feedback and insights revolve largely around the security risks and vulnerabilities that such a language could do.

If you are interested, I highly recommend reading through these threads right now, the first two include comments from Adam Back, creator of Hashcash which is the proof-of-work used in Bitcoin.

– Turing complete language vs non-Turing complete (Ethereum vs Bitcoin)
– letstalkbitcoin on committed tx, homomorphic value, fungibility, privacy
– Will turing compleastness allow contracts to contain viruses and malware that could affect the network in unforeseen ways?
– Adam Back about Ethereum and security risks