  We present high-resolution measurements of the coefficient of thermal
expansion $\alpha (T)=\partial \ln l(T)/\partial T$ of the quasi-twodimensional
(quasi-2D) salts $\kappa$-(BEDT-TTF)$_2$X with X = Cu(NCS)$_2$, Cu[N(CN)$_2$]Br
and Cu[N(CN)$_2$]Cl. At intermediate temperatures (B), distinct anomalies
reminiscent of second-order phase transitions have been found at $T^\ast = 38$
K and 45 K for the superconducting X = Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br salts,
respectively. Most interestingly, we find that the signs of the uniaxial
pressure coefficients of $T^\ast$ are strictly anticorrelated with those of
$T_c$. We propose that $T^\ast$ marks the transition to a spin-density-wave
(SDW) state forming on minor, quasi-1D parts of the Fermi surface. Our results
are compatible with two competing order parameters that form on disjunct
portions of the Fermi surface. At elevated temperatures (C), all compounds show
$\alpha (T)$ anomalies that can be identified with a kinetic, glass-like
transition where, below a characteristic temperature $T_g$, disorder in the
orientational degrees of freedom of the terminal ethylene groups becomes frozen
in. We argue that the degree of disorder increases on going from the X =
Cu(NCS)$_2$ to Cu[N(CN)$_2$]Br and the Cu[N(CN)$_2$]Cl salt. Our results
provide a natural explanation for the unusual time- and cooling-rate
dependencies of the ground-state properties in the hydrogenated and deuterated
Cu[N(CN)$_2$]Br salts reported in the literature.
