DK and Mouser have a "report errors" button, and when you fill out the info, they send you a polite, apologetic email indicating the error will be fixed. (I'm not sure how automated these systems are, if it's a form letter, or the things actually get fixed in due time; but they do look at them and take them seriously. At least a few have been followed up with a "yes that looks wrong, it has been corrected" message.)
As for shipping errors, call up customer service. These aren't the cheapest distributors, and most of what you're paying for is convenience: stocking, quality, quick shipping and customer service. Make use of it!
Typically, they'll send the item again, free of charge, don't worry about returning the mistaken item. Occasionally the problem is deeper than that (the wrong item has been stocked) and a third try is necessary.
I've never been shipped completely wrong parts, like someone crossed orders or something, but I suppose that might be possible; they might ask for return shipping in that case.
I would guess shipped errors are less than 1 in 100, which is typical for the service industry. (YMMV, I'm sure others have had poorer experience, and still others have never had a mistake -- keep in mind you need to average over all these cases, not rely on just your own personal experience.)
Tim