So when you complete a career and get a specialization in each of the skills taken do you get a specialization even in non-career skills you might have taken?

I believe it is a no. That is certainly how we have been playing. If someone knows different than I am more than happy to change.

Pg 46 of the players guide:

The character learns a free specialization for each of that careers key skills he trained during his time in that career.

The errata states that it does /not/ include those gained at character creation (only those after play starts).

jh

Yup, anything taken -before- XP is earned does not matter in your first career transition, and I assume that is why you get freebie specs if you spend the CP's to get more skills.