Deadheading air carrier Captain reported noticing from his seat in the cabin that the aircraft had not been properly de-iced; and contacted the flight crew who made the decision to return to the gate at TYS for a more effective de-ice procedure.

Narrative

I was deadheading on FLT XXXX TYS-ZZZ when I observed the following from my seat. In the de ice pad after type 1 fluid was applied I heard the flaps extend and looked out my window at the top of the left wing and observed copious amounts of snow still on the wings. I assumed they lowered the flaps to clean the underside. Several minutes later I noticed what appeared to be very small amounts of type 4 fluid applied over the snow; with some patches of snow still white on both the top surface of the wings and the leading edge devices. The winglets were untouched and completely white with snow. Again an emphasis on the tiny amounts of type 4 fluid applied over many patches of snow. Large swaths of the wings appeared completely devoid of any type 4 fluid. Unfortunately I did not observe the actual application of the fluid; only the aftermath. As we pulled away from the de ice pad on our way to the departure runway I left my seat and approached the forward flight attendant (FA) and said I needed to talk to the flight crew. I informed the First Officer (FO) via the interphone that they needed to inspect the wings before takeoff. The FO then came back into the cabin to look at the wings and we subsequently returned to the de ice pad for a redo.The second de ice job was much better; the wings were properly cleared before the type 4 and the fluid looked uniform and completely covering all critical surfaces that I could observe. Then we sat there for a very long time in active snowfall while the de ice crew looked for a ladder to do a post spray inspection (from Captain PA). Unfortunately I did not time the events but after quite some time I start to notice signs that the fluid was becoming saturated with snow. I could see white patches of snow building up in places and the fluid was losing its sheen. I again went forward and informed the flight crew of my observations via the interphone. We then returned to the gate to refuel and start the process all over.