I've often done full-flap side-slips in 172s, 177s and 182s without any effect on the elevator/stabilizer. However there was an effect on my non-pilot passengers on one flight and I now have a policy of side slips, only when solo or with a pilot passenger!
Some aircraft, particularly gliders, have unreliable airspeed indicators when slipping. The key is to ignore this and just maintain the pitch attitude, or slightly drop the nose a little, for an added safety factor.