Some way to represent all the hazzards of dealing with alien and prototype technology.
Lab incidents should kill some people and force the lab to shut down for some time. Some of the research projects should get a random set back. It can also destroy one of the items being researched forcing you to hunt that one once again
Workshop incidents should be the same. It can also destroy some of the materials used in production.
On the other hand - those quite nasty events could be balanced by adding some breakthroughs (geting a fixed amount of research points or some bonus to research speed). With workshop a good event can result in saving some of the materials, increasing speed of production for a while or just getting some fixed bonus to currently produced item.
To further expand this idea other 'screens' can also get some events:
Hangars/garrages can sustain some damage from badly placed missile or fire or any other related bad thingy. Vehicles could just get malfunctioning. Planes getting unscheduled maintainance works etc. As a good event you can get a faster repair/reload/refuel speed of currently attended vehicle/plane or getting an instant repair.
Soldier\personel screen could have some medical/training related moments. For example a soldier suddenly getting thick and being transfered to medcenter for a day or two. Or some of the soldiers losing points due to not participating in missions (those who sit at base doing nothing). Good event could give us some minor random skill improvement, getting healed faster or even promotions.
This is a huge thing to do and will probably fit Cris`s idea of 'thermometer' rather than a simple suggestion. I thing that having a random event directly touching you and your forces might be interesting. Your thoughs?