I've made perhaps a mistake in my lab today. When splitting cells,
before adding trypsin I washed them with 10 ml of pure Fetal Bovine
serum solutin (FBS) instead of PBS (phosphate buffered solution).Then
I incubated the cells in DMEM at 37C. I did have difficluty separating
the cells from the flask's wall, but tapped them and they seemed to
disadhere. Will my cells culture properly? Any ideas what might
happen?

FBS contains an inhibitor of trypsin, did you wash it all out
thoroughly prior to trypsinizing?
If you tapped them a bit too hard you might have damaged some cells,
where they clumped together after you had them disadhear? Did you
pipette them to break up these clumps?

I'm betting that you'll be fine, maybe a longer growth curve if you
had damaged cells.