The barrel needs more triangles. Lots more. A pretty decent rule of thumb is, twice the radius, 1.5 times the sides. Now I know you don't have the triangles to work with 10+ sides on most things, but you could use 6, 9, 12 and 15 or something (12/15 for the barrel, 6 for the thin tubes on the side, 8 for the thicker parts…