What skills and abilities are required for product management that aren't taught in an MBA?

Product management is one of the roles where you wear multiple hats, often at the same time. Most of the answers below would give you a rough idea of the hats that you will wear -- 1. Futurist - Defining and evangelizing what's next for the product. 2. Get done - Project management, Coordination 3. Evangelizer - Act as a spokesperson internally and externally for the product 4. Technologist - Hack an experience to convince people, take a crack at the bug fix that is rightly not prioritized but still needs to get done, understand and question technical architecture at a high level. 5. Analytics - Measure: what's happening with the product? What do the metrics mean? 6. Resource manager - Choose what should be prioritized. Coordinate with tech lead on getting the right person for the right job with a focus on getting the right experience to customers asap! This is in no way comprehensive. But, it gives you an idea of things you need to work on beyond business school. My main focus would be super strong analytics, something far more rigorous than the data analyses classes in b-schools, and building technology products, including developing your coding skills. Building your products also give you an idea of thinking from the customer etc, basics on UX and the various steps that are involved from idea to execution and measuring and iteration. Showing great products you built in b-school, or sharing learnings from what you built are key strengths that you can carry forward beyond the b-school.

Design. Not just UX, but the tenets of good design. This doesn't need to be in depth, but rather breadth. A good starting point is something like Design for Hackers. Reading Dieter Rams is excellent resource too, as is Sketching User Experiences (I know you mentioned UX design in your question - just thought I'd offer an additional resource). Customer development is incredibly important as well. This is one of the most effective ways of achieving product/market fit.

Learn to code.  If they are technical, then drop out and found a company. Barring that, actually doing something - anything! - while in school is useful.  I printed and sold t-shirts just for fun, and I learned a lot about inventory risk that now lives inside my bones. That said, you guys have the best lean startup prof in the country.  What does he say?

So essentially breadth is preferred over depth as far as skills are concerned. One may be strong in a specific aspect (coding, design, marketing etc ..) but really they should know a lot about all the various aspects of a technology product along with business insight (market, profitability, competition etc)

A reasonably accurate description of a product managers in high tech: http://product-wisdom.com/

I've seen many graduating MBAs struggle in a new Product Manager job because they leave school believing that people should just follow them and do what they ask because they are the PM. A few areas around 'soft skills' would be extremely helpful: How to influence and guide a team of stakeholders Managing meetings efficiently and effectively How to lead with confidence (not arrogance)

I would say a good project manager should be able to identify what works best for users. Stuffing features won't make it the best product however the right features will drive users to your product. Basically he should know where to draw  the line in terms of features and usability. For this it's important to do a comparative analysis of other products available in the market and find out which features people want to use and if they are available in the industry or not. Then accommodating those relevant features in the right manner would be one of the most important ability of a product manager. I don't know the appropriate term for this "Quality" but I learnt this overtime with a brilliant product manager.