So, making the assumptions that all of the ecn/eco are actually because of drawing/drafting errors not folks knowing how to read a drawing... and so concentrating on the drafting aspect:
1. Set the expectations of the drafters - if nothing else invoke relevant industry standards (iso or asme etc.) and make it clear that drawings are expected to comply with them and show a good level of completeness etc. Make sure copies of the standard are available to staff for reference.
2. If appropriate some education/training for the drafters but I'll be honest with you, I think this element generally gets over rated/over used because it's 'easy' in so much as you get them some online training software or a weeks gd&t course and say 'they're trained now - problem fixed - my goal for the year complete...
3. Drawing check. However, don't just use drawing check as an inspection process to verify the drawing is complete, complies with industry standards and doesn't have obvious errors. Also use it as part of a manufacturability review and also most importantly use it as an ongoing education/training tool. Make sure the person making the mistakes is the one fixing them - the intent being they learn from having to fix problems. You need to strike a balance between the checker/check process being unpleasant enough that it insentivizes folks to do it right first time, but no so horrible they avoid it at all costs or even quit etc. You need the right person to be doing the checking highly skilled, highly experienced and with the right temperament. It doesn't have to be a 100% dedicated checker but the person/people doing it need the experience and discipline etc. to do it well. Peer review is better than nothing but is only as good as the 'peer' doing the reviewing and the time they have to spend on it - so in the OP situation I doubt it would achieve much.
(Why I think training is over rated as a solution - well I learned to draft & GD&T etc. with little to no formal training, not even some self paced on line classes. However it was made clear to me that I was expected to make drawings and they needed to be good. So I looked at other 'good drawings', asked questions, read standards, got my drawings bled on by experienced checkers/peer reviewers and for an all too brief time period worked with an excellent checker who I learnt a lot from. On the other hand, just before I joined my current employer they had a week's worth of GD&T training, and yet most of them are still useless as they haven't taken the initiative to run with it.)
Posting guidelines faq731-376 (probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484