My wife is a professional freelance translator. She translates from English to her mother tongue which is Dutch. Mostly the translation houses that she does the work for, do all the proofreading.
Occasionally she has to proofread her own work (which she doesn't like doing)and on all occasions she does a spellcheck and grammar check,and then prints the work out and proofreads the hard copy.
She also gets work to proofread from other translators who have done work for the agencies. Very often she is appalled at the standard of some of the translators.
She has a degree in both English and Dutch.