The more natural thing for this sentence would be to use "that", and it is almost certainly the error you are being asked to fix:
"I used to work for a company that manufactured automatic processing machines."
You can use "who" to refer to animals, especially when talking to them. "Who's a good dog?" (wag, wag, bark!) "That's right, you are!"
But companies are "it" and "that"...or possibly "they".
"Have you seen the latest video game from Bungie? They really are rehashing Halo, I don't see much new in it."
Changing "machines" to "machine" would not be correct at all. Although if the company really only made one thing, you might say:
"I used to work for a company that manufactured an automatic processing machine."
This would most likely suggest that the company only made instances of one model of this machine (as opposed to the idea that they'd only made one machine, ever). They might--as @Jim points out--manufacture other things.
Note that you can use other ways to refer to "companies". For instance:
From the people who brought you "Finding Nemo" and "Toy Story" comes an all-new animated adventure...
From the studio who brought you "Finding Nemo" and "Toy Story" comes an all-new animated adventure...
That's another case where you'd use that instead of who.