I'm on well water too so I know all about the clogging of the screens.
Have you replaced your well filter in awhile? Its best to change it every 6 months, I changed mine again last week, and my Maytag dishwasher is running great and have never had to clean the water inlet valve screen on mine as of yet.
Can it really fail and cause a flood (like those water supply valves on toilets)?
Yup, its funny you mentioned that because the fill valve in my toilet went bad and the water kept coming out and if it wasn't for the overflow tube in the toilet tank then I'd have a flood in my bathroom. I bought a new Fluidmaster 400A fill valve at Walmart for under $10 and installed it myself in my toilet tank and it works great!
That's why I just wanted you to keep your eye on your dishwasher to make sure that water inlet valve doesn't flood your kitchen. If I was you yes I'd replace the water inlet valve on your dishwasher.
When you click the link to your water inlet valve I posted above there will be a "HOW TO VIDEO" there to show you how to replace it.
Jake