For reference, the two papers are

[1] W. Feller. <A HREF="https://doi.org/10.1090/S0002-9947-1954-0063607-6 ">Diffusion processes in one dimension,</A> Trans. Amer. Math. Soc. **97**, 1-31 (1954).     
[2] A. D. Wentzell. <A HREF="https://doi.org/10.1137/1104014">On boundary conditions for multidimensional diffusion processes,</A> Theor. Probability Appl. **4**, 164-177 (1959).

Differential operators with boundary conditions containing diffusion terms were introduced by Feller [1] for one-dimensional diffusion and by Wentzell [2] for higher dimensions. I am not aware of any error in [1]. Perhaps the lecturer in the OP was referring to the limitation to one dimension in Feller's work?