In the Internet-of-Things (IoT) era, there is an increasing trend to enable intelligent behavior in edge computing sensors. Thus, a new generation of smart wearable devices for health monitoring is being developed, able to perform complex Digital Signal Processing (DSP) routines that extract features of clinical relevance from the acquired data. These new edge computing sensors for personalized healthcare must operate within a tight energy envelope; addressing the ensuing challenge, we herein introduce an inexact and heterogeneous edge computing architecture, specifically tailored to the bio-DSP domain. We observe that bio-signal analysis applications present task-level parallelism, intensive computational hotspots and a high degree of resilience towards errors. These characteristics drive our new bio-DSP edge node architecture design composed of multiple processing cores, a Coarse-Grained Reconfigurable Array (CGRA) accelerator, and hardware-software co-design support to become resilient to a non-zero probability of bit-flips at runtime. All these characteristics enable our new bio-DSP architecture to operate with an ultra-low voltage operating point. Indeed our results indicate that the energy benefits attained from the inclusion of all these characteristics in bio-DSP architectures are more than additive: task parallelism is harnessed both at the processor and the accelerator level, and the high tolerance of the CGRA towards voltage down-scaling is exploited to further decrease the IoT edge bio-DSP system energy envelope.