Is there a certain day/days you're worried about? I looked at the forecast for the next week and I don't really see anything out of the ordinary "possible thunderstorms/rain at some point during the day." That's the standard forecast. You might see a passing shower, or you might not. I don't think you have anything to worry about at this point. Like others have said, people should always be prepared for rain when they head to Disney World -- have at least 2 pair of shoes for each person; lots of socks if you're wearing sneakers; newspaper to stuff in the wet shoes overnight (please don't use the dryers in the laundry room to dry shoes. If you forget newspaper, call housekeeping for extra hand towels and washcloths, they will work well, too.); good rain poncho (the cheap ones work fine for quick showers, but if you experience an all day rain event you'll want something better.); clothespins to be able to hang up rain ponchos in your room; and extra clothing (unless you plan to do laundry anyway).
I'll share our experience with rain at Disney. It was May 2009. Two days before we arrived, the forecast for the week was actually all sunny with a chance of a passing rain shower a few days during the week. The day before we arrived, the forecast for arrival day was changed to increased showers possible. We got there and it was nice and sunny. We headed to EP and spent several hours there in the sunshine. The clouds started rolling in after dinner so we headed back to the resort. It started raining on our ride to the resort. That evening, the forecast for the next day changed to showers on and off all day. It rained pretty much all day. We still went to the parks. By that evening, the forecast for the next day changed to rain off and on all day. We went straight to the gift shop and bought the Disney rain ponchos because it was clear our cheap ponchos weren't going to cut it. Every day the forecast for the next day changed from "mostly sunny" to "rain off and on all day". And this wasn't "pleasant" rain, it was all out down pours. One day we got off the monorail at MK and as we were coming down the ramp, we couldn't even see The Contemporary in the distance and when we got to the bottom of the ramp, we had to walk through water that was well over our ankles. A front stalled over central FL and stayed put for 10 days. Orlando got about 10" of rain while we were there. Even the guys on the Weather Channel were saying, "This is not the week to be at Disney World." Instead of us having the usual sunny all day with brief rain showers every afternoon, we had rain most of the day with a brief break of sunshine every day. Fortunately I was prepared and other than the good rain ponchos, I had packed everything we needed. Despite all of that rain, it was a great trip. The rain kept the local guests away, so parks were not crowded. Lines for rides were very short. People were cancelling their ADRs constantly because they didn't want to go out in the rain, so you could get some really good ADRs at the last minute. We did things on that trip we had never done before because we spent a lot more time at indoor attractions/shows. While I wouldn't wish for anyone to have rain for their entire vacation (and I did feel really bad for those people who were on their once-in-a-lifetime trips that week), it doesn't need to ruin the vacation. Be flexible; make the best of it; and have a great time.