Simple idea. Once a day, ONE of your planets will have something available to analyse.
This will be completely random, and any of your planets may be selected each time.
The event will be minor, and will last for 24 hours - here's an example:

Derelict craft: A derelict craft has crashed into the planet's surface. You may assign a portion of your workforce to investigate it. (If analysed) -20% production, you receive a random, uncommon/NPC drop artifact (eg planet flux potentially) (Perhaps the less OP mission artis too) after 8 hours.

Hostile forces: A fleet of *Insert NPC faction here* ships have been preying on transports coming out of the planet *Planet name*. Destroy them. -50% production, selected NPCs appear more frequently, after X NPCs of that race are destroyed, your planet's production goes back to normal, and you receive a faction related drop and/or a massive credit bonus.

Meteor incoming: A meteor is incoming to your planet *planet name* - destroy it before it lands, or it will cause untold damage. A meteor appears on your BT. You have a limited time to destroy it. If you do, you get a mineral bonus and some PF. If you don't, it will destroy ALL researched buildings on the planet, BUT increase the planet's mineral production by 4 levels for 2 days.

These are just examples, but I hope you get the idea.

permanant random effects require clicking the analyze button on the planet
temporary random effects are automaticly found, reported, and activated