Carrier-density-dependent internal optical loss sets an upper limit for operating temperatures and considerably reduces the characteristic temperature of a quantum dot (QD) laser. Such a loss also constrains the shallowest potential well depth and the smallest tolerable size of a QD at which the lasing can be attained. In a laser with a single layer of QDs, this loss can strongly limit the output power and cause a rollover of the light-current curve; it also imposes limitations on the conventional method of determining the internal quantum efficiency. Excited-state-mediated capture of carriers from the waveguide into the QD ground-state places a fundamental limitation on ground-state lasing - the output power saturates at high injection currents. The saturation power is controlled by the transition time between the excited- and ground-state in a QD. The longest, cut-off transition time exists, beyond which no ground-state lasing is possible. The maximum number of longitudinal modes that can oscillate in a QD laser increases with increasing surface density of QDs and remains limited (first increases and then decreases) with increasing scatter in the QD-size. In addition to the maximum tolerable scatter, there also exists the minimum scatter in the QD-size for each higher-order mode to start lasing.