When I destroy the defences of the AI, it will often start rebuilding mines on nearby asteroids. This is quite alright, however when I destroy the constructor they are left with 0 hit points. Having eradicated the rest of the enemy presence, they still remain, blocking my own exploitation of the asteroids. I suggest making all the 0-hitpoint asteroid mines auto-scuttle once the colony on the main planet is destroyed to fix the problem.
Well known and I believe to be remedied with Beta 4

For now, you can still target the 0% structures. It's tricky on asteroids because half the time it's the asteroid itself and you need to be careful with where you click to point to the building
on the asteroid

A comment on the AI as well; I played on medium. I was severely beaten in the early game, losing all my frigates three times while gaining very little on the enemy, probably because I did not focus enough on military in the start. However, the AI never exploited its advantage, it could have easily moved on to destroy either of my two new colonies that had only one gauss defence platform each, but seemed to prefer to wait for me to initiate the battle once again. In fact the pirates presented by far the most dangerous attacks I encountered. I also noticed that it never built a trade port, causing it to lag a lot economically.
AI issues have been beaten with a club pretty severely in Beta 3

Also well known, and right now the AI is very basic and dumb. The devs are working on it!