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In this paper, we introduce the MIDI Degradation Toolkit (MDTK), containing functions which take as input a musical excerpt (a set of notes with pitch, onset time, and duration), and return a ``degraded'' version of that excerpt with some error (or errors) introduced. Using the toolkit, we create the Altered and Corrupted MIDI Excerpts dataset version 1.0 (ACME v1.0), and propose four tasks of increasing difficulty to detect, classify, locate, and correct the degradations. We hypothesize that models trained for these tasks can be useful in (for example) improving automatic music transcription performance if applied as a post-processing step. To that end, MDTK includes a script that measures the distribution of different types of errors in a transcription, and creates a degraded dataset with similar properties. MDTK's degradations can also be applied dynamically to a dataset during training (with or without the above script), generating novel degraded excerpts each epoch. MDTK could also be used to test the robustness of any system designed to take MIDI (or similar) data as input (e.g. systems designed for voice separation, metrical alignment, or chord detection) to such transcription errors or otherwise noisy data. The toolkit and dataset are both publicly available online, and we encourage contribution and feedback from the community.