What's the meaning of "learned a thing or twelve"?

The phrase learned a thing or twelve isn't an idiom.

A thing or two is a common way of saying one or two things (or less precisely a few things).

The author has tweaked that phrase, replacing two with twelve. This not only increases the meaning from a few things to several things or many things, but by altering a more common phrase, it draws attention to the increase by differing from what a reader familiar with the original phrase might have anticipated.

So to sum up, you could reword your original sentence as:

And in those 10 years I can say that I may have learned several (or many) things.