Question: I've noticed an increasing number of jobs that are asking for experience with data mining and business intelligence technologies. This sounds like an incredibly broad topic but where would one go if they wanted to develop at least a partial understanding of this stuff if it were to come up in an interview?

Answer: 
Go read [Data Mining: Practical Machine Learning Tools and Techniques (Second Edition)](http://www.cs.waikato.ac.nz/~ml/weka/book.html).
Then use [Weka](http://www.cs.waikato.ac.nz/~ml/weka/index.html) on a pet project. Despite the name, this is a good book, and the Weka package has several levels of entry into the data-m... er machine-learning world.
Maybe you can also try to work with real BI - it is almost impossible to get in contact with data-filled and running SAS, MS, Oracle etc. I work in a team which integrates BI BellaDati for enterprises. For try-out and personal purposes it is free with some datastore limitations ( <http://www.trgiman.eu/en/belladati/product/personal> ).

BellaDati is also used as a learning tool on technical universities focused on practical application of data mining and analysis. The final manager-level dashboards examples of BellaDati can be seen at <http://mercato.belladati.com/bi/mercato/show/worldexchanges>

You can work here with SQL datasources, flat files, web services and play. From my own experience - to show real samples of market analysis practise (like case study etc.) is good for an interview.

I wish you luck,
Peter