Flooring Tile - Removing carpet tack strip from concrete slab

I'm in the process of removing carpeting from a concrete-slab constructed home in preparation for the laying of ceramic tile. When I removed the tack strip some of the nail heads broke off leaving the nail in the concrete. Should I be concerned that these nails could pop up and create problems in the future as far as cracking the newly laid tile? If so, how can these nails be removed? I've tried a claw hammer, pliers, vice grips, etc. and there just isn't enough to grab. Some are headless and some have been driven too far into the concrete.

Also, should I be concerned with the holes left after the removal of the nails? Concrete chipped away everywhere there was a nail. If these need to be patched, what should I use?

just pound those stems down with your hammer or cut them off with a dremel or similar.
fill in the holes with thinset as you tile.