I am in f1 status, I have filed 1040ez for 4 years now, but this time in addition I had 1042S, which I could not file becos 1040ez does not have it. It was very small amount 60$. What can be the problems?

You are not supposed to file 1040 when you are on a F1 student visa. Always file 1040 NR or 1040 NR EZ.

Check 1040 NR instructions on page 44 under Amended Return.
http://www.irs.gov/pub/irs-pdf/i1040nr.pdf

Thanks for the info, but it seems I can correct only 3 years, and I have used this for 4 years now. When I renew my visa or move to a different status, can I just own up for the error and pay whatever I owe them?

Page 49, pub 519. I think you can file amended returns for any year. Just that you won't get a credit or refund if you file later than 3 years.

See pg 64 Pub 519 for "getting help". Also see pub 17, pg 18.

File Form 1040. Report 1042S income on line 7 (add with W-2 income) or line 21 (other income).

Is there any penalty that I have to pay? Can I request to waive such things?