There's no real silver bullet other than applying the systems engineering process diligently. You start by writing down your user requirements (what the system needs to deliver), and you follow the thread of figuring out that "to do X, this subsystem has to provide conditions A, B, C..." recursively, in a breadth-first search. The level of detail codified in these functional, performance and interface requirements depends on the level of assurance you need.

Then, you need to validate that each requirement is met by your system. This can be done by test, analysis (mathematically proving some property), review of design, or inspection. It's true that you can't fully validate most space systems on Earth, because we can't simulate all environmental conditions simultaneously. That's why you ideally you want each requirement to be validated by two methods.

When you find anomalies due to integration effects, it's usually because your interface requirements are not specified well enough ;)