After removing the carpet in my living room I discovered one pretty uneven spot. In the uneven spot I ended up using self leveling compound which worked good.

Now after I have all the new plywood down I have a few areas with 1/16 or less of a gap, when I use a long level.

My question is 1/16 a workable gap when installing hardwood floor. I'm installing 3/4 Maple hardwood.

Are you referring to low or high spots in the subfloor? If that's the case you're fine, but I would try to use a longer device to measure the high and low spots, like a straight one or 2" x 4".

Yes the low and high spots and with a 2x4 I have low spots of up to 1/16. But now found one high spot on one of the beams that is 1/4 of an inch.

I'm thinking about taking out the nails and shaving it down by 1/4.

Or what is the best solution? If shaving what tool could I use?

You would be fine by simply sanding the high spot down rather than going through the trouble of removing the plywood...maybe you didn't say that? What kind of self leveling compound did you use? I've always avoided that with wood sub floors as it can break apart/crumble, potentially causing unneeded noise underneath when walked on.