But if you were applying for a position at another firm, what would they likely look at to determine competency?

I'm not a lawyer - but my guess would be how many cases they've handled in the past, whether those were with another firm or by themselves (not sure what this is called - if anything - "self-employed lawyer"?), and how the case turned out and such (though this latter thing may not tell you much - after all, they could be a great lawyer and candidate, but lose every single case not based on anything they did or didn't do).

As you can probably tell - I really don't know what I am talking about in this area...

Then how would you go about identifying a competent attorney?

The bar exam is different than what doctors go through