What is causing the erratic sine wave in my Hartley oscillator?
To make an oscillator to oscillate one must have an amp and feedback circuit which meet Barkhausen criteria - at certain frequency the total phase shift of the amp+feedback circuit is 0 or a multiple of 360 degrees and the amp amplifies at least as much as the feedback circuit attenuates. To get the oscillator to start the amp must amplify a little more than the feedback attenuates. Unfortunately the output amplitude grows until the amp distorts and that's also your case. Pure sine output needs an automatic gain limiting circuit (=AGC) which reduces the gain just to the exact balance with the feedback attenuation when the amplitude is good, but not too high causing distortion. Your oscillator hasn't such circuit. The amp distorts, it cannot output more.
LC circuit filters the result a little rounder than rectangular, but it's not sine, it has plenty of harmonic components. Math design of the circuit is needed to make the LC filtering so effective that the harmonic components are low enough without AGC circuit. An AGC circuit would make it work perfectly. It can make an oscillator to work so well that low distortion sine is possible even without LC filter, only RC phase shift feedback is needed.