Mortgage can last a lifetime and that extra 1% can add up to literally thousands of dollars over the years. I have friends that are in their 70s and still paying off their home loans. It'll pay off in the long run to make sure you find the best deal possible. Don't let poor credit stop you from refinancing your home.
There is a refinancing myth that says you should not refinance your mortgage unless your interest rate will be at least two points less. This myth is not necessarily true if there are other benefits to the refinance or other reasons behind it.
You can ask for a copy of your settlement cost papers (the HUD-1 form) one day in advance of your loan closing. This will give you a chance to review the documents and verify the terms.
If your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.