What security threats does blockchain technology solve or present? I am interested in security, identity and authenticity in electronic networks. 

What sort of security concerns could blockchain technology help with and what sort does it pose? 

Are there entry and exit security concerns?
The problem Bitcoin solves

Bitcoin provides a method for tracking scarce digital assets. This was previously solved by central entities providing an authenticator role and exerting control. Bitcoin solves this problem by creating a truth source from network consensus. Besides for its payment application, this truth source can be employed in a number of different ways, such as proof of existence, identity management, and due to its limited supply perhaps as a digital gold. 

By nature, decentral systems are inefficient: For a big entity, i.e. countries or companies, with reasonable grounds to trust their own central truth source, there are more efficient ways of accounting their monetary flows.

Blockchains in general are only as valuable as they are secure, so I think it will be unlikely that there will be numerous competing services based on different blockchains, rather I think that there will be few, and additional services built on top of them, in the fashion of Colored Coins or sidechains.

Blockchain Security Vulnerabilities

As moshaholo already said the only known fundamental vulnerabilities are double-spending and majority attacks. While these are currently reasonably unlikely in Bitcoin, other blockchain projects with less hashpower have turned to implement additional measures to protect their integrity: 


Alternative Mining algorithm, e.g. Merged Mining, Scrypt, X11, X13, X15, NIST5, POS, SHA-3, multialgorithm mining
Alternative Difficulty adjustment algorithms, e.g. Kimoto Gravity Well
Extensive Checkpointing


There may be bugs in Bitcoin Core that haven't been discovered yet, however the implementation of alternative client software is helping to uncover unexpected behaviour as the network matures.

Lesser problems include that correct time cannot be enforced on the network, traceability of payments can lead to reduced fungibility and loss of privacy.

Are there entry and exit security concerns?

While interaction on the blockchain is secure and mostly trustless, there are challenges with


wallet security
exchanging currency for bitcoin: counter-party risk, fraud by charge-back, scams
verifying authenticity of business partner's information


Identity on the network

As every user can use as many addresses as they want, identity on the network can be fairly private or as public as one wants. Privacy takes some effort, as one can reveal common ownership of addresses e.g. by using them together as inputs for a transaction, or by creating obvious change outputs.