Talking about EM 'Immunity' (assuming this is what you mean by 'radiations'): immunity is hardly correlated with one or the other concept. While in theory there is no explicit clocik line in the asynchronous design (for real-world implementation my expectations are different), which might be especially vulnerable to 'received' interference, interference may cause significant problems in an asynchronous design where input 'signals' are expected to be constant during some calculation.
Overall, it is hard to decide whether asynchronous or synchronous designs are more vulnerable regarding interference. I'd expect not much difference (if any) beween the concepts on terms of immunity.
Regarding the 'other problems': race conditions are one of the serious issues when designing asynchronous logic.