For me, they wanted copies of the marriage license and a divorce certificate. More later, I'm on my cell phone
Sorry to take so long.
They required the above, and although I had my divorce certificate I didn't have a copy of my marriage license. They waited until I ordered and got one, and mailed it to them. (I applied online, so we mailed things back and forth.). I think they may have asked for a copy of my birth certificate too; I don't recall. When they were done with these papers, they mailed them back to me immediately.
Here's a list of things you may need:
Social Security Forms - Information You Need to Apply for Spouse's or Divorced Spouse's Benefits - Form SSA-2
If you apply online, they will mail you information about what to send. It took about a week and a half before I could send off all this stuff, but once I did, the response was great. I still didn't know how much I would be getting, until I logged into the SS website and it was listed there. Then about a week after that, it was direct deposited and has been deposited like clockwork ever since.
Anyway, I thought they were very easy to deal with. I applied online on June 9th, the day after my birthday, and had money in the bank on July 11th. Direct deposits have occurred like clockwork on the second Wednesday of each month. The day it arrives depends on your birthday. You do not need to contact your ex-spouse at any point during this application.
Here is another URL that includes a link for applying online, and that answered my other questions including questions of eligibility:
http://www.ssa.gov/retire2/divspouse.htm
As for pitfalls, I think that the most important thing is to wait until your FRA (age 66 for me) if you want your own SS to remain growing until age 70 (assuming you plan to switch over to it at that time). I wouldn't have thought that waiting until after my 66th birthday would matter so much but it did.
Another pitfall is the personal, emotional pitfall. I didn't know it would be so hard to do this but I found all of this dredged up the past a bit and was distressing. However, as soon as the money hit the bank the problems were over for me.
Hope this helps!