Why do my pot lights flicker randomly when not at full brightness?
Dimmers have to be compatible with the types of lights in use. The bog standard dimmers that have been in use for years generally work fine for incandescent type bulbs and the halogens that work at direct line voltage. 

With the advent of CFLs (compact florescent lamps), low voltage halogens and LED types it talks special types of dimmers for these to be used in a variable brightness mode. Do note that not all items are even dimmable and you can get into serious overheating issues in either the dimmer switch or in the light module if you try to operate with a dimmer. Similar issues can happen when a non-compatible type of dimmer is in use. 

My suggestion for you, if you need to keep the mix of light source types, is to convert over to simply using a switched on-off control instead of dimming. If dimming is desired then switch all of the light sources on the circuit to the same type and then select a dimmer that is compatible with that type of lamp. Modern dimmers should show on their box what types of lamps they should work with. In the realm of the light sources themselves you may need to do some additional research to determine if a particular low voltage halogen, CFL or LED lamp assembly is actually dimmable. It may come down to specifically only purchasing items that are marked as dimmable on the box or product information sheet.