We present a local, distributed algorithm to detect measurement errors and infer missing readings in environmental applications of wireless sensor networks. To bypass issues of non-stationarity in environmental data streams, each sensor-processor node learns statistical distributions of differences between its readings and the readings of its neighbors, as well as differences between its current and previous readings. Scalar physical quantities such as air temperature, soil moisture, and light flux naturally display a great degree of spatiotemporal coherence, which in turn leads to a spectrum of fluctuations between adjacent or consecutive measurements characterized by small variances. This permits stable estimation over a small state space. The estimated distributions of differences are then used in statistical significance tests that exclude rare random errors in measurements at any single sensor, and to infer missing readings. Compared to an alternative method based on Bayesian classifiers, our algorithm is more storage-efficient, learns faster, and is more robust in the face of non-stationary phenomena. Field results from a wireless sensor network deployed at Sevilleta National Wildlife Refuge are presented.