Others have addressed the (almost) real time updates of MLS comps available to Realtors. Let me talk about the listing process, and some of the other aspects of using comparable sales.
You mention that you want to list your home, but you didn't say whether you have spoken to any agents yet. An agent speaking to you about listing your home should be prepared with comparable sales, and should be capable of taking you through what they mean for the pricing of your home. Some agents will come to the first meeting with a full CMA worked out for you. My preference is to come to that first meeting with a general picture of past sales in the area, get a detailed picture of the positives and negatives of your specific property, and then come back with an analysis of the closest comparables and a pricing recommendation. Either way, an agent who cannot speak intelligently to the comps may be someone you don't want to use.
The first question you need to ask about a comp is whether the sale is truly comparable to the home you are considering (either as buyer or seller). Factors which might rule out an otherwise good comp include location (even within the same town), property size, property condition, upgrades the seller may have made, and damage or environmental issues. While it is possible to make adjustments for these factors, you are often better off finding a more suitable comparable when possible. For example, if you have a 1,500 sf 4 bedroom home with a mold issue, a 3,000 sf 4 bedroom with no problems is probably not a good comparable.
The next question you need to address, especially in our current market, is what were the conditions of the sale? A seller on the brink of foreclosure might take an offer that a homeowner who is in good shape with his mortgage would refuse.
The final question is when did the comparable sale take place, and what has happened to the market in the meantime. What has happened to the market is influenced by national factors, such as interest rates and the availability of mortgage loans, as well as purely local factors, such as the number of homes on the market at any given time.
Your best bet would be to work with a Realtor who has experience working with sales comps, and who generally has access to better and more timely information than you can get.