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@slallum, That does seem to be a problem, though I do observe that the issue reported by bdb with CalledProcessError is no longer an issue:
>>> import subprocess, pickle
>>> try:
... subprocess.check_call(['python', '-c', 'raise SystemExit(1)'])
... except Exception as e:
... pickle.loads(pickle.dumps(e))
... 
CalledProcessError(1, ['python', '-c', 'raise SystemExit(1)'])
Looking into how CalledProcessError is defined (https://github.com/python/cpython/blob/79db11ce99332d62917be9d03b31494b1ff2f96a/Lib/subprocess.py#L60) may shed some light on the recommended way to make a pickleable Exception class that takes more than one argument.
Hmm. It seems it does it by not calling the superclass __init__. Indeed, following that model it seems to work:
import pickle
class MultipleArgumentsError(Exception):
 def __init__(self, a, b):
 self.a = a
 self.b = b
err = pickle.loads(pickle.dumps(MultipleArgumentsError('a', 'b')))
assert err.a == 'a'
assert err.b == 'b'