Yes, if the earth was the center of the solar system, the motions of the planets would be much more complicated and would seem to slow down, stop, reverse, and speed up again for no apparent reason. Also there is the problem of the parallax of the stars, where the stars shift position as the year progresses.
This was explained by putting the planets on epicircles (like the sun on the flat earth model, except perpendicular to the surface of the earth and saddle shaped). This still wasn't accurate enough, so another theory put the planets on orbits around the sun while the sun still orbited the earth (Tychonic). This theory matched up very well with observations and was acceptable to the geocentrics.
Eventually it became possible to see the parallax of the stars, which could only be explained by the motion of the earth around the sun in the heliocentric model instead of the Tychonic.
The round earth model easily and simply explains the observations. But for the flat earth model, the planets would probably have to be madly swinging back and forth past the sun, and the stars would have to be on separate transparent shells that shift positions in ways that make it look exactly as if the earth is round and orbiting a ridiculously giant ball of infernal plasma.
If the flat earth model is correct, it would almost seem as if God is trying to play a trick on us.