Additive Manufacturing Engineer here.
To start off, what aspect of 3D printing do you want to be apart of? Do you want to stick with the plastics and do rapid prototyping? Do you want to move to DLP/SLS/DMLP/DMP - so many names for practically the same thing - and do near net parts and production grade? There is a lot going on in the additive manufacturing industry and you need to know what you want before jumping in.
Above all else you need to be proficient at modeling. The free modeling software suggested here is a starting point, but no one will take you serious unless you have experience with industry software such as Solidworks, Auto Cad, Creo, NX, etc. Next, having experience with MAGICS is a big plus, We have one engineer who basically lives and breaths MAGICS, and to go against your assumption that it's only used for laser printing techniques, we use it to fix STLs for our Fortus FDM machine.
If you're looking to go to the industrial side and design functional parts you need to understand the mechanics that go into it. You need to understand thermodynamics, material properties, traditional manufacturing process, statics/dynamics, etc. It's ridiculous the amount of times I have to reflect back upon things I learned in school that I thought I would never use. Also, having a broad spectrum of knowledge on applications is very useful because this technology is being utilized in every facet of industry.
Getting the job done is only half the battle, being able to communicate with employers, peers, and customers is a big part of my job. You have to know the technology and the applications and be able to convey that information in a way that both technical and non technical people can understand.
Let me know if this helps or if you have any more questions.