I have an issue where the vertices on my project glitch and create spikes any time I move another vertice I have an issue where certain vertices that are moved trigger another vertice to spike away from the object and move out of place. Once it has spiked, it mimics the moment of the vertice I original was trying to move.If I try to put back the spiked vertice, it moves another vertice. Sometimes selecting proportional editing puts the spiked vertice back in place, but it will move again on the next adjustment.
This can happen when you use Mirror Editing with non-uniform rotation.

Disable Mirror Editing (up in the toolbar) and make sure you have rotation applied before you use it.
Object > Apply > Rotation