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.
When it comes to lowering your rates you will need to weight the benefits of having a lower rate vs. paying points up front. You may end up paying a lot more depending on your choice and how long you plan on keeping your mortgage.
These days most people request a Good Faith Estimate (GFE), but have no clue what to look for on the GFE. Make sure you request a GFE that has ALL fees estimated and disclosed. This includes: origination points, processing, lender, appraisal, title, escrow... ALL FEES... especially the Yield Spread Premium or YSP.
When evaluating different lender offers, in the mortgage loan pre-approval process, pay closest attention to the interest rates they are offering & the closing costs. These are the two biggest factors that will help you figure out which lender is right for you. If one of these two factors is too high, it could offset the benefit of refinancing for you.