Any passages I should spot check for heresy?
All of them. In other words, never let your guard down with any Bible translation. Always be vigilant in case there is ever a passage that comes up with a translation or interpretation that is heretical.
I wasn't aware that you could read Greek.
I can't although I actually tried to learn once.
It’s not easy to teach oneself. The fundamentals aren’t actually that hard, but there are enough exceptions to the rules that all but the brightest need an experienced translator to guide them.
There’s a story they told in my Greek class about an English shepherd boy who taught himself biblical Greek. One day he went skipping into town and quoting from the text, and the townspeople wanted to burn him as a witch because they believed it impossible to teach oneself Greek without the aid of the devil.
A couple of other points:
-The KJV (or as the non-barbarians call it, the Authorized Version) gets a lot of traction in some Orthodox circles because it used Byzantine manuscripts as its NT base text.
-Some might quibble about the NRSV being the most accurate translation. It is certainly not the most literal, though a literal rendering does not always make the best translation...But translation philosophies and the discussion of them are generally over-discussed.
-If you are going to buy a Bible, get one that you will actually read, not one that someone on the Internet thinks you should. Instead of worrying about potential heresy in a Bible (here I make a big dramatic eyeroll), if you come across a passage that you think is at odds with your Orthodox faith, ask someone, you know WWMSFD?
I say all of this not as an authority but as a layman who can read biblical Greek passably well for sentences at a time and then stare at a page absolutely baffled at what I am reading.