Historically, Law and Chaos sort of represented "us" and "them" and OD&D was quite vague about how Law=Good and Evil=Chaos, or if this wasn't intended at all. In my campaign I tend to go with a simple alignment system where Good and Law are pretty much the same thing, while Evil and Chaos are pretty much the other thing. While this doesn't mean that DCC has to interpret alignment in this way, it might frame a starting point for discussion. AD&D expanded alignment into the more familar two-axis system where good-evil could be graphed against law-chaos to obtain more options. DCC returns to a more simplistic model, one similar to that of OD&D, and so I tend to look at it from a more global view rather than getting as specific as AD&D.
I would rule that a trap isn't good or evil, any more so than one could argue that gravity is evil since I could fall down and hurt myself. I think that the intent of Detect Evil is to identify the presence of evil creatures and evil artifacts if the artifact is sentient. Thus, I would rule that Elric's blade Stormbringer would be detected but a pit or spike trap would not.
My player's Neutral cleric cast Detect Evil last night. What is the opposing alignment to Neutral? Should I ignore Lawful & Chaotic creatures & just allow the spell to detect threats to the cleric?
I rule that the Neutral caster can detect both ways, but has to specify if he is detecting good or detecting evil.