Traditional machine translation (MT) metrics provide an average measure of translation quality that is insensitive to the long tail of behavioral problems. Examples include translation of numbers, physical units, dropped content and hallucinations. These errors, which occur rarely and unpredictably in Neural Machine Translation (NMT), greatly undermine the reliability of state-of-the-art MT systems. Consequently, it is important to have visibility into these problems during model development.Towards this end, we introduce SALTED, a specifications-based framework for behavioral testing of NMT models. At the core of our approach is the use of high-precision detectors that flag errors (or alternatively, verify output correctness) between a source sentence and a system output. These detectors provide fine-grained measurements of long-tail errors, providing a trustworthy view of problems that were previously invisible. We demonstrate that such detectors could be used not just to identify salient long-tail errors in MT systems, but also for higher-recall filtering of the training data, fixing targeted errors with model fine-tuning in NMT and generating novel data for metamorphic testing to elicit further bugs in models.