Air carrier First Officer reported a failure of the MCI de-ice crew to properly de-ice the aircraft prior to take off.

Narrative

On Day 0; I was the First Officer serving flight from MCI to ZZZ and we encountered serious de-icing shortcomings with the staff at Kansas City International Airport. We flew Aircraft X into MCI the previous night and it had sat on the ramp; collecting snow and ice for several hours. Upon doing the walk-around; I noticed a severe amount of ice accumulated on the tail and the wings; with icicles even underneath the wing trailing edges; engine cowlings; and vertical stabilizer. I brought this to the attention of the Captain and we discussed that we were going to do a full body de-ice once we taxied to the de-ice pad. We also agreed to do a pre-contamination check. Anti-ice would not be required since it was clear outside. Once we reached the de-icing pad around XA:30; we configured the aircraft and the de-icing process commenced. After the team finished; I walked back to the cabin and did my pre-contamination check. The left side wing was clean but the right side wing was not. On the right wing; I noticed thick ice still remaining on the trailing edge with the same icicles I spotted during the walk around. I also noticed lots of partially melted ice; slush on the top surface of the right wing. Once I entered the flight deck again; I relayed this information to the Captain and we called the de-ice truck back out to the aircraft to re-spray the wings again. About an hour later; I did a second pre-contamination check and determined both wings to be clean. We departed shortly after without incident.This was a massive safety oversight on behalf of the MCI de-icing crew. It is critical for them to spray the aircraft completely and correctly as well as to check that all ice has been cleared. Especially on the wings and tail. An aircraft simply cannot depart safely with any ice on the wings and our collective decision to conduct a pre-contamination check uncovered a serious critical error. I recommend better training and procedures for de-icing personnel at Kansas City International Airport (MCI).