What algorithms or methods can be used for the tracking of audio pitch contours? (Such as in musical vibrato and glissando, or for tonal vowels in languages such as Chinese?). Will a PLL work even for pitched tones that have a weak or missing fundamental? Or is there a more suitable tracking method?
I think a PLL would be hard to use for pitch detection in singing or speech. For the reasons you mention (classic phase/frequency comparators output garbage when the waveforms are too different due to a missing f0), but also because you'll need another method anyway for tracking the large changes in pitch or the switch to voice/unvoiced that would put a PLL off the tracks.
A baseline system could be to extract a pitch on small frames with a classic f0 detector (autocorrelation, AMDF, YIN, or any auditory model), and then use dynamic programming (or from another point of view, the Viterbi algorithm on a HMM whose states are discretized pitch values) to recover a pitch track. A ready to use Matlab implementation for this (auditory model + viterbi) is available here or (fancy autocorrelation flavour + dynamic programming) here.
This will be discretized on both the time and pitch axes, but you could then interpolate.