No, it's the "simple evaluation" that's the common uninformed mistake. The presence of a "squared" term doesn't necessarily mean that you have to multiply by both factors in the term.

The VELOCITY has units of ft/second.

The VELOCITY increases at the rate of 32 (Ft/Sec)PER SECOND

After 10 seconds, the VELOCITY has been increasing for 10 seconds, at the rate of 32 Ft/Sec^2 during EACH OF THE TEN SECONDS, so the first "seconds" factor in the "seconds^2" is PART OF THE RESULT, not part of the calculation, and the velocity is 320 Ft/SECOND. ONLY the SECOND SECONDS FACTOR is applied in the calculation, since THE FIRST SECONDS FACTOR is included in the "dimensions" of the answer.

In your calculation:
If calculated by squareing the seconds, the results are:
after 1 sec velocity is 32*1^2 = 32ft/sec
after 2 sec velocity is 32*2^2 = 128ft/sec
after 3 sec velocity is 32*3^2 = 288ft/sec
after 4 sec velocity is 32*4^2 = 512ft/sec

You have an error in dimensions, since multiplying Ft/Sec^2 by Sec^2 MUST GIVE A RESULT WITH FEET AS IT'S ONLY DIMENSION, and the answer wanted has dimensions of FEET PER SECOND. Obviously an amateur mistake, but not one you should take personally, since it's common.

You can't get an answer in "feet only" other than perhaps the distance fallen. Due to the constantly changing velocity, this requires an integration rather than a multiplication, with the result that the distance fallen after a time "t" is (g*t^2)/2. After falling for 4 seconds, the velocity would be 4*32 = 128 FEET PER SECOND, and the distance fallen would be 32*4*4/2 = 256 FEET.

"Feet per Second Squared" is the CORRECT VALUE AND DIMENSION for the acceleration of gravity. Not science, but mathematical definition.

As shown, you can get the wrong answer using the right information if you don't really understand simple mechanics and/or math; and sometimes you can even get the right answer using the wrong information, if you include a suitible compensating error.

A technique, by the way, commonly used in engineering is finding an "error" - commonly called a "fudge factor" - that will account for the unknown errors in input data. It can be quite effective, and properly done can be quite reliable. One can even interpret the "g" constant as "the fudge factor required to make velocity equal to the integral of acceleration over a time interval when the acceleration is due to local gravity."

John