Ab initio molecular electronic structure computations of thiophene-based compounds constitute an active field of research prompted by the growing interest in low-cost materials for organic electronic devices. In particular, the modeling of electronically excited states and other time-dependent phenomena has moved toward the description of more realistic albeit challenging systems. We demonstrate that due to its underlying approximations, time-dependent density functional theory predicts results that are qualitatively incorrect for thiophene and thienoacenes, although not for oligothiophene chains. The failure includes spurious state inversion and excitation characters, wrong distribution of oscillator strengths and erroneous potential energy surfaces. We briefly analyze possible origins of this behavior and identify alternative methods that alleviate these problems.