Valves.. take time to warm up, heat can cause badly selected components close to the valve to give drift - essentially, capacitors and resistors have thermal charactaristics which are usually given as PPM/degree C (parts per million per degree C) which the value will change by.. Polypropylene film capacitors are in the order of -200ppm/C - one needs to calculate possible temperature variations, and what effect this will have on the circuits stability.. but you need to do these calculations for any circuit, be it valve or semiconductor.
Trimmer capacitors can have quite bad thermal charactaristics(+/- 500ppm/C), as can potentiometers(+/- 250ppm/C for Cermet, +/- 500ppm/C for carbon), so care must be taken in selection and placing of these.. 'Standard' metal film MF12 and MF25 resistors have +/- 50ppm/C.
Waveshaping: Best to look at this in combination with whatever hetrodyning mixer circuit you adopt.. (assuming you are going for a conventional Theremin) .. The Jaycar / EPE Theremin has one of the simplest designs I have seen, using biasing of the MC1496 mixer to give waveform and symetry controls - This is quite a neat solution, as the MC1496 is quite a good balanced modulator, and certainly beats the simple diode mixer used in the Moog Etherwave.. However, it takes a bit of care to set up.
You can do wave shaping either before, in, or after the mixer - the 'before' option is the most tricky.. There is only one Theremin I know of which uses this scheme, the Moog 201 - Waveshaping is done by selectively filtering the high frequency signals from pitch and reference oscillators.. say the pitch osc fundamental frequency is 200kHz, and goes up to 205kHz.. Filters tuned to 200, 400, 600.. kHz will effectively, when mixed, allow harmonics F,2,3.. to be mixed... and produce audio with these selected harmonics only...
Post mixer waveshaping is easiest.. get the audio (out of the mixer), produce a square wave with a zero-crossing detector, shape this wave as you wish, mix this/these back into the original waveform in whatever proportion suits your taste..
The Etherwave has an extremely simple squaring / distortion scheme where the gain and bias to the transconductance amplifier (VCA) is varied - and people seem quite happy with this (see HotRodEtherwav.pdf .. I cant find a link right now, but Google for it..)
Last - there is the VCO/VCF method.. From the audio output of the mixer, on drives a pitch-to-voltage converter.. Then use this voltage(via an exponential converter unless you use a phase-locked-loop system for your VCO) to drive a VCO, and you can have your VCO generate any waveform you want.. This voltage can also drive a VCF for filtering of this waveform.
There are so many links to Theremin design etc, that I dont know which to give.. But perhaps the best starting point is to read all the articles by Bob Moog, get your head 'round his designs..