Embedded systems in critical domains, such as automotive, aviation, space domains, are often required to guarantee both functional and temporal correctness. Considering transient faults, fault analysis and mitigation approaches are implemented at various levels of the system design, in order to maintain the functional correctness. However, transient faults and their mitigation methods have a timing impact, which can affect the temporal correctness of the system. In this work, we expose the functional and the timing implications of transient faults for critical systems. More precisely, we initially highlight the timing effect of transient faults occurring in the combinational and sequential logic of a processor. Furthermore, we propose a full stack vulnerability analysis that drives the design of selective hardware-based mitigation for real-time applications. Last, we study the timing impact of software-based reliability mitigation methods applied in a COTS GPU, using a fault tolerant middleware.